Hmmm. About the only thing I can offer at this point is hoping that Company B is among the tiny handful of companies that do not drug test. I believe veteran member "jeffman" has a thread somewhere in the forum that contains a link to some database of companies that dont drug test. You can probably do a search of jeffmans threads/posts and try to locate that thread.

How sweet is the offer of company B in comparison to Company A? (ie; salary rate, benefit packages, working conditions, etc)