Which Game Uses the Term "Bulley"?

Billiards (specifically 9-Ball).

In billiards terminology, a "bulley" (also spelled "baulky" or "baulk") refers to the baulk area—the region between the baulk line and the bottom cushion on a British-style (English) billiards or snooker table. In 9-Ball (and other pool games played on such tables), the cue ball is placed "in hand" within the baulk (the "D" area) after a foul or for the break.

The term is British; American pool uses "kitchen" (area behind head string). "Bulley" is an older/dialect variant of "baulk."