Since the Bowling alley and the bar inside are one business(with one business license and one liquor license, staying out of the bar area is useless.
If the entire business does not derive the majority of its income from alcohol sales to be consumed by the glass, you can legally CC anywhere in the place. Obviously if the opposite is true, CC anywhere in the bowling alley would be illegal since it would meet the legal definition of a bar in 28.425o
Can you CC in an Applebees? Sure. Can you CC in the bar area of an Applebees? Of course. It is one business, the fact they have two distinct areas in the business is of no consequence. Same with fill in the blank restaurant (Olive Garden, BW3's, Dave and Busters the list goes on and on..all have bar areas).