Love the mirror idea. I have one on my desk at work, although in my case it's so I can see who just came in the door without turning around in my chair.
Although the onus is on the OP for this (as she acknowledged), I do think it's telling that everyone else in the office is able to adapt and accommodate it, and only this one person refuses to--even though that one person is bothered by the OP's startle reflex, and notices she does it often. If I were the supervisor in this case I think I would first try modifying my own behavior in a minor way, as the other employees have done, rather than yelling at my worker to stop it.
I mean, yeah, some people do the "OH! You startled me! I am so sensitive!" thing to get attention, but after a few events I think it becomes apparent if that's their motivation, or some other eye-rolling situation. For example I had a co-worker who startled easily because she zoned out when she should have been paying attention. Once we were working side-by-side on a project and we had to wait for something to finish, so we just sat there silently for about a minute. When it was done I started to speak and she JUMPED and was like, "Oh, you scared me!" Um, I've been sitting here the whole time talking to you!
But I would think it would be obvious after a while that the OP was genuinely startled and upset by that, so I don't see what's to be gained by yelling at her. But, obviously, one can't really change the supervisor's behavior, so I would go with the mirror, making people open the door, something jingly on the door, a sign asking people to make noise as they approach, etc.. If you have any say at all in where your new work area would be, I would try to find a better setup, at least where you don't have your back to the door. I think it wouldn't hurt to politely ask if this was possible, anyway. If your supervisor has anything to do with assigning work areas, that might be a good way to broach the subject with her--"As you've noticed, I startle easily, and I know that's annoying to people. Is there any way I could get a work area where I'm facing the door, so I can see people coming?"