A bra purse is usually a small fabric pouch you can attach to your bra strap with a piece of velcro. This is the most discreet of hiding places and by far the safest - but that doesn't make it the best.
There are certainly advantages to using a bra wallet. I can be relatively convenient if it's attached to your shoulder strap because you can actually access it (on the other hand if it's on the back or under your arm, forget it).
It's also the most lightweight of the various travel money belts and definitely the cheapest, since there's virtually nothing to it.
The disadvantage is obvious - you'll need to go somewhere private to access your money. That said, you shouldn't be delving into any undercover money belts during the day: you should keep a small amount of cash in an accessible place, such as your pocket or bag, as long as it's an amount you're prepared to lose. In the unlikely eventuality you should get mugged or pickpocketed, handing over your day stash should satisfy most petty thieves, for whom speed is essential. The rest of your money will stay safe and absolutely out of sight.
Still, a little bra pocket is really too small to be a proper security item. Like the ankle wallet, you can't fit a passport into it and if you fill it up too much, it will show.
It's also flimsy and some models are easy to tear.
Some women clip it to their underwear although in that case, why not simply use a regular travel money belt?