Hi J.,
any form of irritation, whether it be bubble bath, bar soap, friction, can start the symptoms of a UTI. These are not viruses, but bacteria being introduced into the urethra. Otherwise, antibiotics would not help us get rid of them.
My doc once told me that the act of peeing in the water, is enough to give a child a UTI when taking a bubble bath. you open the doorway and bacteria, be it from your body, existing already on the tub surface (I know i don't disinfect my tub before each bath...) can enter and start the vicious circle. Also irritants play a big role as well. try to make sure your 3 yr old doesn't pee in the water, and to make sure she pee's after the bath... this will help flush out bacteria and irritants before they can take hold and cause infection.
I would choose a known mild bubble bath... up until about age 5 (at that point, baths were OUT, and showers were in) I have always used baby bath... it doesn't hold it's bubble factor very long, compared to bubble baths, but i have found that by the time it loses it's bubbles, it's time to get out anyway. After all, long soaks aren't good for the skin. I always followed up with an Aveeno lotion massage. Oh, and I know this sounds elementary, but make sure you rinse the bath water off with clean water before pulling them out, or all that stuff will just sit on their skin and further irritate.
As for you, I second the bath salts... it's not bubbles, but it is very relaxing, soothing for the skin and I have never had any signs of UTI since switching to them.
Good luck!
~J.~