They are awful for a reason apparently, it's too sort out the nutcases from the real nutcases. I had a friend to went through all sorts of problems and ended up on one of those wards, and thought she was mentally fucked up. Then she saw the other people in the ward, and decided she wasn't anywhere near as bad as the other patients, and it helped her turn her life around.
Sounds like you've got a brilliant friend...and from what you tell me she
maaaay quite like you, but of course i havn't seen this with my own eyes so it's hard to judge. I'd suggest you subtly investigate wherever she'd want to date you. If your confident enough, try to some gentle flirting and see what happens.
You could try this: Tell her you want to go somewhere (say...cinema), see what she say's. If she she's interested, then ask her if she wants to invite anyone. If she doesn't want to invite anyone, you've got a date. If she invites her friends, your're in her friendzone
[sub]Disclaimer: If this doesn't work, i'l warn you now that i'm not the most qualified of persons to give this sort of relationship advise.[/sub]