I did a bit of an experiment recently. I diluted a portion of my KOH soap paste with just water. I diluted a second portion of the same paste with a mixture of water and glycerin. The water-only dilution lathered much better than the water-glycerin dilution.
But I'm talking here about the development of bubbles with this experiment, while a decent bubble bath liquid must develop bubbles AND have stable, long lasting bubbles. There's a distinct but important difference, as the shaving soap makers (and users) know all too well.
It's been awhile since I read about the physics of bubble formation. It's pretty amazing. Surface tension, gravity, viscosity, evaporation, etc. all meld together. I'm sure we don't have to know all that much about the science of bubbles to make a great bubble bath, but I'm not really informed about the craft and art of the matter either.