Hi John T;
Welcome to the forum.
Poultry absorbs a lot of smoke quickly. Depending on what flavor bisquette you are using, for my taste 3 hours is the maximum. If this is your first turkey in the Bradley, you may only want to apply 2:20 hours or 2:40 hours.
What size turkey do you have, and what temperature do you plan to cook at? It may take you longer than four hours to fully cook the turkey, unless you butterfly it, or it just a turkey breast. It will take the Bradley a while to get to your set temperature, so that increases your cook time. Even when you preheat, once you open the door and place the turkey in it you lose a lot of heat by opening the door, and the conversion of heat to bring the temperature of the turkey up. It's been a long time since I've used the Bradley for smoking a turkey. When I did I would smoke/roast 15lbs. - 17lbs. turkeys, and I believe that would take me 6 - 8 hours.