I actually do say "bestest" frequently, but always tongue-in-cheek. If my coworker is going out and agrees to pick up lunch for me, I'll certainly tell her "You are the BESTEST!" (She is also in the communications field.)
Don't use it in essays -- of course not -- but you'll hear it. Once you get past the age of 8 or so, you do realize it's not standard (nor is having more than one "best" anything) but you do it because it's fun. The same way I use "ain't."
I guess girls will be girls. Have you ever heard a man use it?