So if I'm hunting bobcats without a trapping license and I shoot one do I still have to bring it in to a fish and game office and if so will be charged for it?

A harvested bobcat must be turned into Fish and Game to have a CITES tag attached to it, regardless of the method of take (this includes salvageed road kill). Yes, you will be charged for the tag and vendor fee. A fee of $2 will be charged for each pelt tag. An additional $1.75 vendor fee will be charged to each license holder when pelts are brought in for tagging.   Josh Royse Magic Valley RCO