Being a mom of four teenagers, I can fully relate to your daughter's aversion to soap and washing. With every one of our children, around that age came a period of time when it was somewhat of a battle to get them to properly care for themselves. Even when we got them to get in the shower, a few of them would come out ten, fifteen minutes later, saying they were done, only to find out they didn't even wash up at all!!! We would have to go so far as to smell their hair, and check their body for signs of dirt still on them!! So, back in the shower we would make them go! Deodorant was not used all the time either, but eventually they all learned the valuable lesson of keeping neat, clean, and well cared for. Now we can't get them out of the shower!!! But that is not to say we weren't on them for a seemingly way too long of a period of time!! We had to stay on top of them, regardless of whether they appreciated it or not, whether they wanted us to or not. Ya, they wanted us to leave them alone, but we didn't. Nor should you in regards to at least making sure she is washed and clean. Shaving and the bra thing can probably wait. She's only eleven. Buy her some training bras if you feel she really needs them, and just put them in her drawer without her knowing. She'll eventually begin wearing them on her own, but don't push it.
If you read up on the subject, you will find this to an extent the norm for kids this age. So remember that, and take your battles with a grain of salt, knowing that this too, shall pass away. As with the terrible two's, the never ending five year old's questions, etc., with patience and understanding, you will be able to gracefully ride this one out, too.
It is important to continue to stress to your daughter the importance to be clean, and continue to encourage her in doing so. She may not particularly like it all the time, but you are still her mother, and you are responsible to find a way to teach her what she must know, and see to it that she eventually learns. Your daughter is probably embarrassed about her changing body, as many kids become. Sharing things gently with her, the changes she is going through, and how it is all very normal will help her out. Be sure she knows however that as her body changes, so do her hygiene needs, thus the greater need for her to shower, use deodorant, etc. Just let her know ahead of time the things that she will be experiencing in the near future, let her know matter of factly that it's normal and nothing to be ashamed about, and that it's ok for her to talk to you about it. That's what you're there for.
I just reread your request and realized you said you still have to wash her hair, she showers, yet she will not let you in her room when she dresses. I would like to let you know it seems to me she is playing a power game with a bit. I also have three points I would like to touch on. #1: She is eleven years old. At that age, I was babysitting children, caring for them, and you are still washing her hair for her??? With all due respect, it seems perhaps you may have created your own monster to an extent here. She should have been weaned from this practice years ago. And when I think back to that age, there is no way I would have wanted my mom seeing my bare body at all!!! #2: You must obviously see her bare body when you wash her hair in the shower, but she won't let you see her as she gets dressed?? This in itself is a contradiction, but it also leads me to point #3: There shouldn't even be an issue with you being in the room with her getting dressed-she's eleven years old, not three. Eleven year olds should not have their mommy in the room with them. Give her her privacy. As she says, "leave her alone". Besides my four teenagers, I also have a six year old who cares for herself fully in the morning from washing up, to dressing, to brushing her teeth, to brushing her hair. There is no need for you to be doing so much for your daughter. To a certain extent, you should leave her alone, to another extent-holding her accountable to washing and bathing herself properly-you shouldn't.
Make her wash her own hair, tell her she must shower herself. If she doesn't, and insists on her continued outright defiance regardless of your insisting, let her know there will be consequences: Some form of a punishment-perhaps no sports game or practice, no night out over her friends, whatever. Something that is important to her. Good luck.