benchrest

bench +‎ rest, since the gun is mounted on a rest placed on a table or bench.

benchrest (plural benchrests)

1. (gun sports) A shooting sport in which very accurate and precise rifles are shot at paper targets.
2. The infrastructure for benchrest.
   • 2004 June, David E. Petzal, “Shoot like a man: There are no benchrests in the wood”, in Field & Stream, volume 109, number 2, page 62:

     Since deer usually give you no time to get into a nice, steady position like sitting, and since there's a shortage of benchrests in the woods, it pays to be able to shoot upright.

• benchrester
• benchrest rifle