Do you think it would be okay if I ask my girlfriend to wear a bra when we go out?
Why do you want her to wear a bra when you go out?
She draws a lot of attention from other men when she's not wearing a bra and it makes me jealous.
I'm sure you are jealous of the attention your girlfriend gets from men when she doesn't wear a bra, but that's not your decision to make. You should talk to her and tell her how you feel. She may change her behavior after your conversation.
But what if she doesn't want to wear one even after I tell her how I feel?
If she still chooses to not wear a bra, that's her decision to make. You're allowed to tell her how you feel, but telling her what to do isn't appropriate.