For 19 years all I had was a tub. Now I have both and I do both. I love the occasional long hot soak with candle light and music. It is a great form of relaxing for me.
As far as genital problems, bladder infections and yeast infections can occure from EITHER bathing or showering. The problem isn't bathing, it is soap and other means of cleaning that get in the vaginal area and doesn't get rinsed away thoroughly. And if it gets in the urethra, it travels to the bladder and results in a wicked UTI and/or bladder infection.
My mother (a stroke victim) requires help to get clean and I am forever having to remind my Papa the importance of rinsing her well. She likes it best when I shower her for that very reason. I get the whole girl thing.