You mention noise in the "wee hours in my backyard." Imagine for a moment that you were not TWO STREETS from the bowling alley, but instead 50 feet from it. Imagine the noise level then!!! Certainly you, of all people, can understand our concerns!
one, you obviously haven't been to Mexquite on Friday evenings during happy hour, the parking lot is packed, the restuarant almost empty, and the bar is standing room only consuming whatever it is that is being sold cheap, I would guess beer and margharitas.
I thought the hill behind the store was more than 50 ft just in elevation change (which believe it or not, will have a greater impact on the noise that reaches your home). As to how noisy it will be, that depends a lot on the amount of insulation the place has and the actual volume level of noise inside. If it is too noisy after they open, then you can complain to the city council to have something done to limit the noise to reasonable levels per already established noise ordinances against disturbing the peace.