+1.
I keep a spare bra/underwear in with my hygeine supplies in a desk drawer. They are underneath, way in the back. I'm a little nervous, though, because every other Wednesday the child psychiatrist who helped me get this job uses my office and we share the desk drawers. He does not use the drawer with my stuff. He's a kindly man in his seventies, and I don't think he'd be freaked out by seeing a bra, but still...
When I was teaching, I had a stand alone closet with one side where you could hang stuff, with a shelf above. The other side was for book storage. I kept lots of stuff there, a strapless bra that could be worn with anything, a pair of black flats, a black jacket, and hygeine stuff. I was always freaked out when I would open the closet to get books out. The bra and such were hidden, but not totally out of sight. No students ever saw it, though!