Since you know the bacteria is e coli, that points to her not being cleaned correctly after a bowel movement. E coli lives in the lower intestine. When it comes out in feces, sometimes it can be pushed up into the urethra and cause a bladder infection.
It sounds like when you are wiping her clean, some of the fecal matter is going in to the urethra. Try wiping from front to back, so that you aren't dragging any feces over her urethra opening.
If this is the second time I would suggest you look at a cause , is hse drinking plenty of liquids as dehydration can cause UTI's ...is she looked after by yourself , does she have a good appetite and seem happy ?