What is “bull-dance”?

Solution 1:

The phrase appears to be mid 19th century slang referring to a generic men-only dance, rather than a specific one. Likewise, the etymology is most likely using bull as a generic male animal, similar to stag in stag party. E.g.

Bull-dance. A dance in which only men take part: cf. Stag-dance, Gander-party, Hen-party, etc. — A dictionary of slang and colloquial English, 1905 (also lists ram-reel as another synonym).

Or

Stag. Adjectival meaning "pertaining to or composed of males only" (as in stag party) is American English slang from 1848. Compare bull-dance, slang for one performed by men only (1845); gander (n.) also was used in the same sense. — Online Etymology Dictionary

It's also worth noting that historically the best known literal Bull Dance is probably Minoan Bull Leaping (ταυροκαθάψια), a form of non-violent bull fighting that survives in Spain as recortes.