My answer with respect to Michael Drosnin and premillenialists will be very different. I believe it is not fair to lump premillenialists together with Bible Code people. Besides, Drosnin is NOT a premillenialist.
First on the Bible Code and specifically its most famous proponent Michael Drosnin. This stuff is sheer, absolute nonsense. This is a clear case of pseudoscience. Drosner uses practically every logical fallacy in the book (please forgive the exaggeration). One can use computer programs to mathematically/statistically "analyze" any text to prove anything one wants. Drosner ignores obvious inconsistencies, he creates false impressions, he abuses the Hebrew language–all with the rather blatant purpose of making a lot of money from gullible people. I am sure Drosner could apply the identical analysis to find the same kind of information in the Wizard of Oz or the latest Robert Ludlum novel. I suggest you google Drosnin and simply read some of the material by his critics–which are many. To be honest, I believe that you do not need to do anything to "refute" Drosnin’s Bible Code. All you need to do is point people who are willing to listen to the Bible. Why are people sucked into such nonsense? That is hard to say. Trying to disprove The Bible Code is kind of like trying to disprove astrology, tarot cards, 2012 or UFOs. Believers in such nonsense are obviously not thinking rationally, in which case logical arguments tend not to be all that helpful. Personally, I think I would just change the subject and try to point people toward the evidence for the Bible, for Christianity and for Jesus Christ. Those who are attracted to such obvious nonsense are clearly looking for something. Hopefully you can present your Christian life and convictions as an alternative. I doubt logically dissection Drosnin’s books will work, but it cannot hurt to acquaint yourself with some of the specific analysis of the critics. I will include some analysis below (and give the web site I got it from
Does pseudoscientific junk like The Bible Code hurt the integrity and validity of biblical scripture? Certainly not! The evidence for biblical inspiration and for the consistency of the Bible’s message is not undermined by such work at all. I suppose that to the extent people read the Bible Code, they might be confused about the point of scripture, but I do not see how Drosnin’s stuff undermines the evidence for the resurrection of Jesus, the scientific or the historical accuracy of the Bible, evidence for legitimate fulfilled Bible prophecy, etc.. I cannot rule out the possibility that if people put their faith in these bogus "prophecies" and later on realize what nonsense it is, they might be tempted to reject all prophcies, including legitimate examples in the Bible. People with a good heart will see through this.
As for premillenialism, like I already said, I feel that, despite the problems and even false teachings of many premilennialists, it is unfair to lump this false doctrine with Bible Code belief. I will not analyze premillenialism here. I have an appendix on the topic in my book Daniel, Prophet to the Nations (www.ipibooks.com). Sincere, rational, reasonable Christian believers have considered premillenialism. As far as I know, no sincere legitimate Christian accept Bible Code thinking. Let us assume for the sake of agrument that premillenial beliefs are not correct, does this doctrine undermine the integrity or validity of scripture? I believe it does not. It is possible to be a saved person and accept this teaching. This is not a salvation issue. One’s opinion about the details of what will happen at the end time does not affect one’s ability to repent, to be a disciple of Jesus or to be a Christian. I do believe that in many churches, the heavy focus on premillenialism is an unhealthy distraction from the important issues of repentance, helping the poor, loving God, discipleship of Jesus, righteousness and the like. For this reason, I am not afraid to publicly teach against premillenialism, but I am not prepared to way that it undermines the integrity or validity of biblical Christianity.
Some material from Wikipedia on Drosnin is copied and pasted below.
John Oakes, PhD
Criticism of Michael Drosnin (taken from Wikipedia)
Journalist Drosnin’s books have been criticized by some who believe that the Bible Code is real but that it cannot predict the future. On Drosnin’s claim of Rabin death, Drosnin wrote in his book "The Bible Code" (published in 1997) on page 120; "Yigal Amir could not be found in advance". This is very telling in that dangerous period of Israeli politics from the Oslo Accords of 1993 to the assassination of Yitzhak Rabin on November 4, 1995.  Critics have noted a huge error in the "code" Drosnin claimed to have found, they note Drosnin used the Biblical verse Deuteronomy 4:42. Scholars note; "For example, citing again the passage intersecting with Rabin: that passage is from Deuteronomy 4:42, but Drosnin ignores the words immediately following "a murderer who will murder." What comes next is the phrase "unwittingly" (biveli da’at). This is because the verse deals with the cities of refuge where accidental killers can find asylum. In this case, then, the message would refer to an accidental killing of (or by) Rabin and it would therefore be wrong. Another message (p. 71) supposedly contains a "complete" description of the terrorist bombing of a bus in Jerusalem on February 25, 1996. It includes the phrase "fire, great noise," but overlooks the fact that the letters which make up those two words are actually part of a larger phrase from Genesis 35:4 which says: "under the terebinth that was near Shechem." If the phrase does tell of a bus bombing, why not take it to indicate that it would be in Nablus, the site of ancient Shechem?" 
Drosnin also made a number of claims and alleged predictions that have since failed. Among the most important, Drosnin clearly states in his book "The Bible Code II", published on December 2, 2002, that there was to be a World War involving a "Atomic Holocaust" that would allegedly be the end of the world. Another claim Drosnin makes in "The Bible Code II" is that the nation of Libya would develop weapons of mass destruction that they would then be given to terrorists who would then use them to attack the West (specifically the United States).  In reality Libya improved relations with the West in 2003 and gave up all their existing weapons of mass destruction programs. A final claim Drosnin made in "The Bible Code II" was that Palestinian Authority leader Yasser Arafat would allegedly be assassinated by being shot to death by gunmen, gunmen Drosnin specifically stated would be from the Palestinian Hamas movement. This prediction by Drosnin also failed, as Yasser Arafat died on November 11, 2004 of what was later declared to be natural causes (specifically a stroke brought on by an unknown infection). The only conspiracy theories about Yasser Arafat allegedly being murdered have been made by a few Palestinian figures, and have involved alleged poisoning that was suppose to have been on the orders of Israeli officials. The only alleged Palestinian collaboration in this conspiracy theory involve two leading Palestinian figures from the Palestinian Fatah movement; those are current Palestinian Authority and Fatah leader Mahmoud Abbas and Mohammed Dahlan the former head of Fatah in Gaza. Writer Randy Ingermanson criticized Drosnin by stating that; "And that’s all they are, even for Drosnin — possibilities. He believes that the future is not fixed, and that the Bible code predicts all possible outcomes. Which makes it not much of a predictive tool, but again, he seems not to mind this very much. If you are laying bets based on Drosnin, you had better be willing to bet on all possible outcomes." 
Some accuse him of factual errors, claiming that he has much support in the scientific community, mistranslating Hebrew words to make his point more convincing, and using the Bible without proving that other books do not have similar codes.
Responding to an explicit challenge from Drosnin, who claimed that other texts such as Moby-Dick would not yield ELS results comparable to the Torah, McKay created a new experiment that was tuned to find many ELS letter arrays in Moby-Dick that relate to modern events, including the assassination of Martin Luther King, Jr. He also found a code relating to the Rabin assassination, containing the assassin’s first and last name and the university he attended, as well as the motive ("Oslo", relating to the Oslo accords). Drosnin and others have responded to these claims, saying the tuning tactics employed by McKay were simply "nonsense", and providing analyses to support their argument that the tables, data and methodologies McKay used to produce the Moby Dick results "simply do not qualify as code tables".
Skeptic Dave Thomas claimed to find other examples in many texts. While Thomas’ methodology was alleged to have been refuted by Robert Haralick and others, Thomas’s criticisms were aimed at Drosnin, whose methodology was actually far worse. (In fact, Drosnin’s example of "Clinton" in his first book violated the basic Bible Code concept of "Minimality"; Drosnin’s "Clinton" was a completely invalid "code"). In addition, McKay claimed that Drosnin had used the flexibility of Hebrew orthography to his advantage, freely mixing classic (no vowels, Y and W strictly consonant) and modern (Y and W used to indicate i and u vowels) modes, as well as variances in spelling of K and T, to reach the desired meaning. In his television series John Safran vs God, Australian television personality John Safran and McKay again demonstrated the "tuning" technique, demonstrating that these techniques could produce "evidence" of the September 11 terrorist attacks on New York in the lyrics of Vanilla Ice‘s repertoire. Additionally, "coded" references in non-Torah Bible texts, as for instance the famous Number of the Beast, do not use the Bible code technique. And, the influence and consequences of scribal errors (eg, misspellings, additions, deletions, misreadings, …) are hard to account for in the context of a Bible coded message left secretly in the text. McKay and others claim that in the absence of an objective measure of quality and an objective way to select test subjects, it is not possible to positively determine whether any particular observation is significant or not. For that reason, most of the serious effort of the skeptics has been focused on the scientific claims of Witztum, Rips and Gans.