Are you sure it's a bunion? I don't mean to doubt you, but I have never heard of a bunion on the outside of a foot.
I have a terribly painful bunion on the inside of my left foot and I wear a splint at night. I've seen them at Walmart as well as Amazon, but as far as I know, they are only made to wear on the inside of your foot. While it seems to help with the pain, it does nothing to fix the problem. The alternative would be surgery and it is really not an option for me.