I'd like to think Bane isn't skeevy enough to have his men undress Selina just to put her in her costume, so I'm assuming she was wearing it under her clothes.
I can believe that Bruce has secret stashes of costumes, probably for the entire family, hidden away practically everywhere in Gotham City for when he needs a quick change.
Either that or he's perfect a gadget that allows for one to instantly transform into their costume .