As Terri stated, make sure there's no soap residue. Make sure there's no soup residue either, though if I were a betta I probably wouldn't mind a little soup for the trip. 3 hours really isn't that long of a time, I often have fish bagged for 3 hours before they leave the house.
Haha, soup residue? First thing that popped into my mind was essence of clam chowder.
But yeah - I would think as long as they were clean they would be fine. Are items like these something you could pick up new at the dollar store or the like? Otherwise, travel coffee\tea mugs? They're insulated some, and they should be available for new, for cheap.