Regardless of the brand of dish soap you use, (other sites claim Palmolive, Ivory, Dawn or other brand), add a small amount of glycerin for blowing bubbles (not for bathing) to make them bigger and more stable. Start with a tiny amount, mix it up, add a little more as you see fit.
Glycerin is harmless, cheap (under $2) at any drug store. You can also spread glycerin, or a 50/50 mix of glycerin and water on your hands (it will take a few minutes to rub in and dry) before doing something that will get them dirty (gardening, working on the car, etc.). When you finish, all the grease and grime will just wash right off, even from your cuticles and fingernails.