Dunno where you live (amend your profile????), slowgrow, but Bougainvillea are tougher than many people think. If you don't go much below 28 degrees in he winter, you might want to put it in a sunny, protected (wind) spot in the ground for a year or two because, frankly, I don't see a bonsai in there yet.
When you do start to prune (and don't remove that lower branch -- shorten it) these things root so well and easily from cuttings that is the better way to go. It's some times awkward to air layer a small branch like that.