Nothing. Music was not like that, nor was dancing like that. Dancing prior to the 20th century was not gyrating, or grinding. Most dances would be akin to ballroom dancing, and many of the ballroom styles, like the waltz gained popularity in the 19th century with composers like Johann Strauss Jr.. Until the Jazz era, nightclubs as you think of them didn't really exist, nor was there a casual place where regular people would just hang out for dancing, as you wouldn't expect music in most places you went. Music was an expensive affair that required you to pay skilled professionals, so music was, for the most part, a luxury of the middle and upper classes.

The exception to this is folk music. Some cultures would have established folk music and folk dances that would take place, typically at weddings, or other ceremonial events, but even those would not involve any rump shaking, and would be comprised of a set number of steps, akin to doing a modern line dance or square dance in many ways. Like Morris Dancing in England, for example, or Italian folk dancing, or others. To the best of my knowledge, these are all dances with set steps, either partnered or not, and never a matter of just getting up and dancing random patterns to music.