Jay, welcome to Susan's.
Here's a thought: If you live in or near a major population center you may have an opportunity to get in touch with a local transgender group whose members might be able to help you with your dilemma. Try a google, you might find something nearby. If all else fails, though, there's still your imagination. That's what I usually used when I was younger, even though I did find some pretty secure hiding spots. A pair of undies and a bra don't take up much space, don't forget.
I realize the fear of getting caught is very real, I lived with it for many years but once it happened, while I was embarrassed as hell, I was also relieved. It turned out OK for me and of course you need to do what's appropriate for yourself in your situation, but don't fret too much. Worrying about it too much will hurt you more than any unwanted discovery will, in the long run.
be careful and, again, welcome!
helen