I think this is a 9 yr old issue all around. I have two boys and getting 8-10 year olds to bathe is ridiculous. They even went as far as pretending to shower by sticking their head under the water and then coming out wrapped in a towel giving the appearance they had washed.
If she is really girly girly then you might try the opposite tactic. Have her help decorate her bathroom and make it the lap of luxury with shaggy carpet throw rugs and a couple big fluffy towels. Especially this time of year you can get cheap "spa" like bath things like special fragrance body washes and bath beads, special shaped soaps etc. Make the bath seem like not so much work but more like something she WANTS to do. Let her know how much you enjoy a bubble bath after a stressful day! To really drive the point home, take her with you to a spa get your fingers and toes done! Show her that the bathing and being clean and comfortable is about her not about something else you REQUIRE her to do.
I did something more simple with my boys. We decorated their bathroom with a nautical theme, I went and splurged on 3 sets of nice fluffy higher quality towels, one red, one blue, one cream and did like a nautica theme. They are in cub scouts so we tied nautical knots in thick rope and hot glued the rope with knots around the mirror. I got a new bath curtain and liner to match the cream towels and we painted the walls a blue grey color like a stormy see. We got a new plusher navy rug for beside the bathtub too. We got a few other things like a chrome shelf and new canvas and chrome clothes hamper and new toilet paper holder. I also invested in a cheap one of those things you hang on the wall in the shower that you pour shampoo conditioner and body wash into. This makes it easy to see what soap you need and easy to dispense, no messing with bottles and reading the labels. (Apparently messing with bottles and opening 3 is too much work!)
Once the bathroom was done, they thought it was soooo cool. Once the bathroom looked nicer and was more of "their" place bath became less of an issue. Having fewer soft fluffy towels also encourages them to bring dirty laundry downstairs more often so the towels will be clean for next time! All in all I spent only like 300 bucks and the house looks nicer too which is a bonus!
Another trick if you can't fix her bathroom up is to let her shower in your bathroom. Usually the parents bathroom has some "better" stigma to it. I think its because usually the master bath is more welcoming, which is why I updated their bathroom and made it "nicer" for them.
Either way it should be a phase, by 14 or 15 she will be showering multiple times a day running up your water bill and driving you nuts and making you late everywhere you go!