In Vaudville, the performers generally had a act that was written, rehearsed, and polished, which they took with them, sets, musical arrangements, and all, from town to town. Burlesque was low budget, though, and Burlesque comics, typically worked and travelled in teams(a la Abbott and Costello)--They worked from a book that they carried with them, which consisted of comic scenes, mostly culled from theatrical plays. which hey would re-stage scenes in each theater, filling out the routine with whoever happened to be hanging around in the theater("Gypsy" fans will remember the scene where the stripper "Mazzeppa" says, "I don't do scenes", whereupon Rose Louise says that she'll do it)--

If you want authentic material, you wouldn't go far wrong but looking up everything that Abbott and Costello did--they were credited with keeping the old burlesque routines alive, because most of their material was straight from the old burleque stage. They didn't literally keep it alive, of course, but they did keep it in front of the national audience, first on the radio, then in films and on TV. There were still comics doing what they had always done on the Burlesque circuit at least into the seventies(I am not an expert in this stuff at all, but I used to run into some of the old performers when I worked on passenger trains back then)--