According to the dictionary, actually, "slow" can be an adverb. http://www.merriam-webster.com/dictionary/slow "Some commentators claim that careful writers avoid the adverb slow, in spite of the fact that it has had over four centuries of usage <have a continent forbearance till the speed of his rage goes slower — Shakespeare>. In actual practice, slow and slowly are not used in quite the same way. Slow is almost always used with verbs that denote movement or action, and it regularly follows the verb it modifies . . ." So, according to that, you could say "drive slow". It is an interesting point. I guess you can make your own decision about whether that is convincing or not. If not, just stick with "drive slowly".

"Drive slowly" is correct grammar. You may run into "drive slow", but not everyone uses correct grammar.

"Drive slowly" is the right answer.