Usually national organizations don't get involved with the state legislations. That generally is up to your state bowhunting organization. In MD our organization, the Maryland Bowhunting Society, successfully lobbied for Sunday hunting in several counties. It was done by members contacting delegates, showing up in large numbers to testify at hearings, and basically taking on the legislators.
The nationals, PBS, Comptons, and Pope and Young are worthwhile to belong to just to keep your ear to the ground as to what is happening nationwide. I know the three have been involved in promoting bowhunting and standing up for bowhunters but on a national level, most recently in discussions of limiting technology in bowhunting.