I want to verify that I can only apply for Bull or Cow moose tag, not both in one year?

You can submit one (1) application for a trophy species during the April application period. When submitting a controlled hunt application, you are allowed to enter two hunt choices. The hunt choices can both be for antlered or antlerless hunts or can be a mix of antlered and antlerless. For additional application rules please see information on pages 32, 36 - 38 in the current Moose, Bighorn Sheep and Mountain Goat proclamation booklets.