Please understand that "meclizine" is just the generic name for Bonine. Rather than buying a small package of Bonine, ask your pharmacist for a bottle of meclizine.
It's the same drug, but you'll get a huge bottle of it for just a few bucks. Much better than paying big dollars for a small pack of Bonine.
I have some serious problems with motion sickness, too, and meclizine has always worked far better for me than Dramamine. I have good luck using the Sea Bands, too, when I fly. (I'm one of the unfortunates who always checks for the little white bag in the seat in front of me when I fly . . . . . )