Like the Rockaway, the Bronco is another dance listed under the "Miscellaneous" category in M.B. Gilbert's Round Dancing (Portland, Maine, 1890) as suitable for either jig time (6/8) or galop time (2/4).
Please see my earlier post on the Rockaway for a discussion of jig and galop rhythms and a sample of jig music.
Leap backward from the right to left foot, 1; leap backward upon the right foot, 2; leap backward upon the left, 3; pass right to side and immediately draw left to right (à la Newport), & 4; pass right to side and draw left to right, & 5; leap forward upon the right, 6; pass left to side and draw right to left, & 7; pass left to side and draw right to left, & 8; four measures. Repeat, commencing as at first. The second time the right foot may move backward at the sixth count, making the turn to the left. Counterpart for lady.
--- Gilbert, Round Dancing, p.165
Reconstruction (8 measures of dance)
(steps for the gentleman; lady dances opposite)
1 2 leap back L, R
3&4 leap back-side-close L-R-L (waltz-galop natural half-turn)
&5 side-close R-L
6&7 leap forward-side-close R-L-R (waltz-galop natural half-turn)
&8 side-close L-R
Repeat from the beginning (4 measures).
This variation has a very similar construction as that of the Rockaway, with a pair of leaps followed by turning steps. The "3&4&5" and "6&7&8" sections are each a waltz-galop with a second side-close added; the dancers make a complete turn every four measures. All steps travel along the line of dance, with quarter turns before and after the first side steps, as described in my previous post on the waltz-galop.
One variation is given: the second time through, the leap on "6" may be backward, resulting in a reverse half-turn instead of a natural half-turn. The pairs of leaps at the beginning are always done backward by the gentleman, make the dance easier for ladies wearing the elaborate bustles of the era.
I have no other English-language sources for the Bronco, but, like the Rockaway, it reappears in American expatriate dancing master [George] Washington Lopp's La Danse, published in Paris in 1903, under the category "Two Step et Three Step". The description is a fairly close translation of Gilbert, but Lopp does not mention the variation of a reverse turn on the repeat.