Now that I can see the enlarged photo, I agree with Elaine, those little black droppings are caterpillar waste (poop)! Army worms leave droppings like that also but I don't think Army Worms bother Bougainvillea plants.
You may have one or more caterpillar's hiding underneath the leaves ... hopefully you can eradicate them so they don't continue to dine on your Bougainvillea.
~ I'm an old gal who still loves playing in the dirt!
~ Playing in the dirt is my therapy ... and I'm in therapy a lot!
Army worms leave droppings like that also but I don't think Army Worms bother Bougainvillea plants. 
