All shrubs, once established, will survive all but extreme drought. Around here, shrubs grow so very large they would block the view of the beautiful bougainvillea flowers. Also, bougainvillea grows quite large -- I mean really large. When I had one on a trellis, I planted daylilies in front of it because they are drought-tolerant, too, and they grow only about 18-24 inches high. Depending on what zone you are in, you could also use bearded iris, as they are very drought tolerant. Unfortunately, they don't do well here in central Florida because the winters are not cold enough for long enough. I'm just not sure shrubs would be good to plant near a bougainvillea unless you have the free-standing type that has been trained to grow as a small tree -- this type will need constant pruning and shaping, and so would any shrub planted near it.