I have a large bougainvillea that I've trained to climb onto an 8ft arbor. From there it runs horizontal. The 8ft stock running up to the top of the arbor is bare (no leaves or shoots). My question is, is there a way prevent the bougainvillea from growing new shoots from the base and stock?
No, not really. You could, in theory, add a geotextile membrane (weed preventer fabric) round the base of the plant, close up against the existing stems, to try to prevent any new growth arising from the roots, but you'd still need to 'rub out' or clip off any shoots coming off the eight feet of stem/s leading to the horizontal growth.