If the pursers' desk does not give out bonine, you might be able to get it in the ship's infirmary. I've had this happen to me and the infirmary had supplies of bonine, aspirin, etc. available that they just gave out to people. No need to see the doctor.
Just to be safe, I always take some with me, though. If you can't find it where you are, maybe try ordering it through drugstore.com or one of the other on-line pharmacy places.
Marty the sometimes queasy