Sources: The Dancing Master 10th Ed. 1698
The Country Dance Book
A 1-4 M1 casts down below C3 and stands between C3, all three facing up. 5-6 W1 casts down below W2 stands between C2, all three facing down. 7-8 Opposites set to one another i.e., M1 to W1, W2 to W3, M2 to M3 B 1-4 C2 and W1 hands 3, while C3 and M1 same, all clockwise 5-8 The same again, counter-clockwise. C 1-8 W1 and C2 hey (W1 face M2 R shoulder) while C3 and M1 same (M1 face W3 R shoulder) the first couple meeting at end so D 1-4 C1 lead down through C3 and cast up into second place. 5-8 C1 lead up through C2 and casts down into the second place.
This is drawn from the video https://www.youtube.com/watch?v=88gjpTi5sQ4
BURY FAIR—triple longways (4/4) (F)
Playford, Dancing Master, I-10, 1698
Sharp, The Country Dance Book, VI, p. 114
Recording: Boston Centre Series, vol. I, by Bare Necessities
A 1-4 1st man casts down below 3rd man & stands btwn. 3rd cu. facing up. 5-6 1st wo. casts down below 2nd wo. & stands btwn. 2nd cu. facing down. 7-8 The two lines set to each other. B 1-4 Hands-3 once round: 2nd cu. & 1st wo./3rd cu. & 1st man. 5-8 Back the other way. C 1-8 Hey across the set: 1st wo. & 2nd cu./1st man & 3rd cu. (passing R-sh. with opp., i.e. R-hd. person), end with 1st cu. in 2nd place (prog.) [[16|steps]]. D 1-4 1st cu. lead down thru 3rd cu. & cast to 2nd place. 5-8 1st cu. lead up thru 2nd cu. & cast to 2nd place.