J. Watlen published in Edinburgh, 1791, a two volume collection entitled 'Circus Tunes'. There are also some tunes of the late 18th and early 19th century that were said to have come from Astley's Circus e.g., Astley's Hornpipe. I think there is a collection of circus music at the Circus World Museum, in Baraboo, Wisconsin, but their website says nothing about it.