How to get really old bugs off the bumper?

Im not sure how much experience you have but if you can snap a photo if there remains paint staining and etching after you clay.
It might be bad enough where you may want to have a pro fix it because its going to require sanding.

 

I'm competant with wet sanding scratches and such but I've only done it by hand. I'm going to do a good clay bar and DA compound, I'll have to see what's left after that and decide if it will require sanding