Here is an idea:
{click to find out about the lady that makes them}
I´d wear something like that either if it doesn´t look like a bra (like the one on the photo), or if it does look enough like a bra to be tongue-in-cheek (yes, my purse is a bra, and no, you can´t touch it). I think the middle ground would be dangerous here, when people would be confused whether the purse is meant to look like a bra, or if it is a bra, or what.