Records of staged bestiality acts extend back into antiquity...and for at least as long have been prone to exaggeration and confusion with fictional or mythical accounts, like the oft-repeated but almost assured erroneous assertion that the Emperor Galba had the poisoner Locusta raped by a specially-trained giraffe. Fiction in this case may be part of the culprit, as Apuleius in The Golden Ass has a (fictional) female poisoner raped by a donkey (the transformed protagonist) before a crowd in the arena.

Given that bestiality has been illegal in most European cultures for large chunks of the time since writing was invented, accounts of actual adult entertainments featuring animals typically only appear in either legal documents or lurid pornography; period newspaper accounts don't appear to mention such acts in any detail, as one might expect.

It is difficult to grasp when exactly the idea got started. In the United States itself, as near as I can tell the idea of sex tourism to Mexico rose to prominence at about the same time as Prohibition (1920-1933) - when American tourists flocked across the border to Mexican towns that were still "wet," several of which featured also featured brothels, prostitution, and live sex shows, sometimes in designated zonas de tolerancia. The more "touristy" Mexican bordertowns would also often feature mules, sometimes painted with stripes to better show up on photographs, which might have added to the idea. I cannot say with 100% certainty that this is where the popular idea of the "donkey show" came from, because even nailing down the earliest accounts is super difficult - the phrase doesn't appear to have entered into common parlance until the 1970s or 80s (with "donkey show" still containing the perfectly normal and unsexual meaning of a display of equines, like a horse show or dog show, making newspaper and case law searches more difficult.)

The idea of a "donkey show" as specifically involving a staged entertainment between a sex worker (usually female) and a mule or horse, usually but not always in Mexico, has gained a lot of popular culture momentum, as shown by films such as Losin' It (1983), Bachelor Party (1984), The 40-Year-Old Virgin (2005), Clerks 2 (2006), The Heartbreak Kid (2007). However, nearly all of the evidence is anecdotal. While there is a sad truth to sexual abuse, and even prostitution of animals - not limited to donkeys and horses - and some evidence for the creation of bestiality films; Luke Ford names a handful of films in A History of X: 100 Years of Sex in Film (1999), and Beetz and Podberseck's Bestiality and Zoophilia: Sexual Relations with Animals (2005) confirms that bestiality was a theme of several Mexican "stag" films of the 1930s, although with dogs. Even with the latter book, I'm skeptical of the accuracy of some of the sources.

The bottom line is some sexual acts between humans and equines have certainly occurred; there is plentiful case evidence (and, regrettably, film) to support that. They may or may not have been organized for private entertainment, in Mexico, the United States, or elsewhere; the illegal nature of the activity, the normal human lack of sexual interest in equines (and vice versa), and the logistics of holding such an entertainment would make documentation difficult (except, of course, for video recording or film). While they may well have been held in isolated instances, given the physical difficulties and social outrageousness involved, it seems unlikely that donkey shows as an organized, reoccurring entertainment were at any point common.

It's really hard to prove a negative, but in this case where all of the evidence is anecdotal, it's also difficult to prove a positive. I can't point to a single, verifiable account of such practices, although there's plenty of anecdotal material.