Outside of the stable yard, it is not common to meet with a bare back rider in Britain. On this tiny island, riding out bareback into the community would be regarded as irresponsible behaviour - especially if something had gone wrong during the ride.
I have never witnessed lessons in riding bareback but I have friends who may from time to time do so when collecting their horses up from the pasture.
In the Welsh valleys it is customary to hold rodeos - that's dropping onto the back of a feral Welch Section C pony - without the help saddle or bridle
The aim of the game is to stay on for more than 5 seconds merely by holding onto a handfull of mane. The organisers me that it is nowadays becoming difficult to get insurance for such competitions since regularly a discarded rider is driven off to the local hospital with a few broken bones. The ponies, brought to the event straight off the moors maybe short but they make good bucking broncos. Hard drinking Welshmen (and the occasional woman) are a breed apart - they even sit differently on the pony.
Maybe it is why our Welsh cousins sing a lot.