There are cosmetics you can use before your tanning application. Since I choose not to cover all my ink for shows, I don't have experience with it because I never took the time to do test runs and figure out what works best. If you do choose this route though, I think it would be best if you don't wait until the night before the show to figure out how to do it.
Dermablend is the product I used to cover my ink for my cousin's engagement party 3 years ago. At the time, my grandfather didn't know that his precious granddaughter's arms were ink covered and I wanted to hide it from him. Nobody at the party knew unless someone told them, at which point they got close to examine my arm and try to "see". It covered well, but it was thick (thicker than foundation) so you have to let it dry. All night I was trying to avoid getting too close to family members in photos because I didn't know if it would rub off on anyones clothes, lol. For a BB show though, your already covered in tanning products so you don't have to worry about that issue.
If it helps, here's a pic of me with the dermablend and another pic of what my ink looks like.