To answer your question, kj_connections, the cruise lines usually provide Bonine on days when the sea is rough (you'll know those days by the appearance of barf bags in the stairwells and other public places). Otherwise, you will have to purchase them - best place to do that is at home before you leave.
First cruise was just 2 weeks ago, Cruise to Nowhere on the Carnival Legend. As my luck would have it, we hit 70-75mph winds. Very very rough seas. My hubby and I both took Bonine, it worked but I still must admit to feeling extremely nervous with those kind of winds.!!!!!!!!!