I wipe excess paint off on a cotton rag or paper towel, which goes home with me. The very little bit that gets swished off in my cup of water gets dumped. Mind you, I don't use cadmium colors - and you would never want to do this with acrylics (plastics) or oils.
Ah- This is indeed my Bagalini bag....and from time to time I've found them at TJMaxx stores for less than retail. You can find them online if you google Bagalini bags. You might get lucky and find one you really like! They make different configurations from small to big. Remember not to go too big....or you'll overfill it and wear out your shoulders!! Good luck finding one - I think you'll be able to find one that suits you perfectly! It's still my favorite for keeping things small and light and yet having everything I really need!