There are many ways to accomplish this. I'll cover the way that I do it. First plan of much more time than you estimate. Due to the slow recovery time for the Bradley to get back up to temperature, it will take more than 2 hours per pound. You may be looking at 18 - 20 hours. A search will give you several ideas on how to do this.
What I do is prep the butt at least 2 hours prior to putting it in the smoker. Prepping the butt up to 24 hours in advance is better. If you prep more than 2 hours in advance, wrap the butt tightly in plastic wrap, put it on a rimmed baking sheet and place in the refrigerator. If you prepare the butt in advance take it out of the refrigerator about 2 hours prior to smoking. I use the "The Renowned Mr. Brown" rub. Some smear the butt with mustard to help the rub adhere to the meat and improve the bark, but I prefer to use either peanut oil or olive oil.
Preheat your smoker and bisquette burner to 275°F if you can get it that high. Place the butt in the smoker, load the bisquette (I like to use 4 hours of pecan), and adjust the oven temperature to 225°F. Typically if I want to serve the pulled pork at 1PM, I will start it at 8PM the previous day. After the smoke has been applied, I will empty the water bowl, and add fresh water (around midnight), and make sure the drip tray is not plugged up. I generally will get up at 4 or 5 AM and check the smoker, and again empty and refresh the water bowl.
I not only go by IT, but also by the texture. The IT is a guideline, I take the butt out when I can slide a dinner fork into the butt, and twist it. If the butt finishes sooner than you had expected, you can use a method that on this forum is called FTC. Wrap the butt in foil, then in a towel that you are not likely to use again for bathing, and place in an empty cooler. This will keep the meat hot and safe for many hours; until ready to pull.
As far as the beans, you could start them at the same time as when you start the butt, but you will need to find a way to cool the beans rapidly, and refrigerate until it is time to reheat. It you cook them both at the same time you can place the beans under the butt to catch the drippings, while you are applying the smoke. I would just check to make sure that the beans are not collecting too many dripping. Or you can put them in the smoker at the end of the cook. If you want to add smoke to the beans, you would have to add more bisquettes.
