I don't see Bullseye listed at CASA or Benton Gun Club (links listed below).
http://www.casarange.com/
http://www.bentongunclub.org/ShootingMatches.html
It is my understanding, from a couple of years ago, that some folks at the Jefferson County Gun Club were doing some type of Bullseye match on select Sunday afternoons; however, I don't know if they are still shooting. They do show NRA rifle matches so they might have a line on any Bullseye matches. You could check with them. If the weather permits us to have an IDPA match this weekend, I may see some members of that club and I'll ask them.
http://www.jeffersoncountygunclub.com/
Looks like you may need to take up rifle shooting.