It will take much longer than the 3 - 4 hours the recipe states. I haven't seen their recipe, so cannot comment directly about it. The issue with the Bradley is that once you place the turkey in the smoker, it will struggle for a few hours just to get back up to 300. Go to Bradley tips for roasting turkey. They pretty much summed up all the the techniques that are mentioned on this board.
Tips For Smoking TurkeyIt will be difficult to get your smoker up to 300°F, and maintain that temperature. I haven't done a whole turkey in the Bradley since many years ago, but recall it took close to 8 hours to fully cook a turkey in the Bradley, and that was an 18 pound bird. When I did this I use a vertical roaster. I use a
Spanek Turkey Vertical Roaster. Their website is difficult to navigate, but they have good products. You still have a whole bird to present, and it cooks faster. Another option to shorten the cooking time is to remove the back bone, then cut the turkey in half, and roast each half on separate trays.
If you have room in the oven on the day you want to serve the turkey, you would be better off using a dual cooking method. That is smoke the turkey for 2 to 3 hours in the Bradley then transfer it to a 325°F preheat kitchen oven, and continue to cook until the thigh meat is at 165°F or your desired higher temperature. This may be another 2 - 3 hours, so plan accordingly. This will also improve the texture of the skin. When poultry is fully cooked in the Bradley the skin will be rubbery.
Also, if you finish in the oven, you can plan to have the turkey finish cooking about one hour prior to serving. Then loosely tent it, and it will stay at a safe temperature for that time. While the turkey is resting, this will give you time to cook or roast your sides.