Answer: Even without seeing your plant, I'm pretty sure you have caterpillars munching on your bougainvillea. I say this because of the black specks you describe. Those black specks are called frass in the insect world - which translates into bug poop. It's a classic sign that caterpillars are feeding. I'm sure they are the same color as the stems and leaves and that's why you can't easily see them. The most effective control for caterpillars is a botanical product called Bt (bacillus thuringensis), sold as Dipel in garden centers. Use according to label directions and you'll rid your bougainvillea of caterpillars.
Best wishes with your garden!
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