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. While W1 casts down below W2 and stands between C2, all three facing down. C2 should come in and move up during the cast. 7-8 Opposites set to one another i.e., M1 to W1, W2 to W3, M2 to M3 (Set fwd and then back) 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 L shoulder) while C3 and M1 same (M1 face W3 L shoulder; L Sh seems to be easiest coming out of ccw circles); 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.