You're better off with a very small dose of Pepto Bismol pills. figure a quarter of a child's dose for a small dog, a full child's dose for a big dog. It's pretty safe stuff (if you're not convinced, call the company and ask).
Bonine (or Antivert or meclizine) -- I don't know how well animals tolerate it. It's a first-generation cycline type antihistimine with antiemetic properties, but it's pretty powerful stuff. I'd not use this med without a Vet who wants to prescribe it for your dog.
Note that the now-discontinued Canadian version of Antivert contained nicotinic acid, and should not be adminstered to animals. DON'T use your old prescriptions in this case.