Subject to subsection (b) of this section, the Board may authorize a bowling alley with 20 lanes or more that has a Class B or Class D license to stay open for bowling and serve food until a specified hour. All alcoholic beverages shall be kept under lock and key from 2 a.m. to 6 a.m. An individual under 18 years old may not be on the premises from 2 a.m. to 6 a.m. unless the individual is accompanied by a spouse, parent, or guardian.