browsing around the net, i found an article dating back to September, 2000, in which the results of a study testing the effect of two common drugs on divers was discussed. 

   basically, "divers" were put on a chamber to simulate a dive to 66 feet (3 atmospheres).  they were then tested for the reactions to pseudoephedrine, a decongestant many divers take to relieve pressure in the sinuses or middle ear, such  as Sudafed, and dimenhydrinate, the active ingredient in most anti-seasickness products such as Dramamine.

   the results?

Even without the drugs, the participants exhibited increased anxiety and decreased verbal fluency at conditions simulating 66 feet under water, the researchers found. Pseudoephedrine produced a slight increase in heart rate and interacted with the depth effect to increase the decline in verbal fluency, but overall, the authors write that "it is unlikely that pseudoephedrine adds significant risk to the diver."

Dimenhydrinate, on the other hand, was associated with much lower scores on a test that required the subjects to switch rapidly between two tasks and is a measure of mental flexibility. "We showed a definite impairment [from dimenhydrinate], especially in combination with narcosis, and the deeper you go, the greater your decline," says O'Toole, an experienced diver who directs the hyperbaric medicine program at the University of Pittsburgh. "I would not recommend that someone take this drug and dive."

  see full story

   so, it would appear that taking any drug containing dimenhydrinate  should be avoided by divers, as this study indicates that it increases the effect of narcosis.

  of course, no one has tested meclizine (the active ingredient in Bonine) to the best of my knowledge ... so ... i guess we take it at our own risk until someone tests it.