I think bras are definitely ugly and mostly used to cover up paint flaws.
There is a company that sells clear plastic paint protection films custom cut to fit different cars. The film is made by 3M and goes on much like window tint. You can't see it except for the lines where it ends if it is installed properly. They have them for bumper covers, hood, and fenders for some Stangs.
You should make whoever painted your bumper redo it and then get that put on.
www.xpel.com