There are few Batwoman costumes on Amazon and eBay. It's Batman Rises Halloween costume for adults. It's black costume, made of polyester, with short corset dress with black cape, headband with bat ears and eye mask.
Image by Dave Monk, CC BY-SA 2.0, Flickr
Who is she actually? Batwoman, in real life Kathy Kane, was introduced for the first time in comic book Detective Comics in 1956. She shows up in other comic books and animated movies too. She doesn't have any superpowers, but she was trained at West Point as a soldier and she masters various martial arts and acrobatics.
She and Batgirl are both part of the Bat family, related to Batman. She lives in Gotham city and helped him on several occasions.
We can find a lot of costumes for Batgirl, who is dressed in similar outfit, but her colors are black and yellow (her Bat logo is yellow).
And how does Batwoman looks like? She is wearing black costume (usually made of polyester and spandex), red belt and ted Bat logo. She has long red hair and sometimes she is hiding behind black mask. She is also wearing red gloves and black and red cape. and that's pretty much it.
You can make that costume at home too - black jumpsuit, black corset or T-shirt with Batwoman logo and red cape. Add high heel boots and you'll look really hot in this outfit.
And don't forget make-up - use black eyeliner and red lipstick and you are ready to party all night.