I have done a lot of grafting, but not on a bougainvillea. Normally the best time is in dormancy, before the new buds swell, but since they are evergreen, your best results would be when in the start of a growth spurt. In our climate that's early summer when I put mine back outside, but in warmer climates it could be as early as March. You don't want to wait for the hot part of summer when the heat can kill the scion, especially in the first couple of weeks when you have it covered with a plastic bag. Great idea though, to get multiple colors on the same plant.

Thank you Hemlock140 for your help. I will try doing so. Unfortunately my winters here are harsh, so I need to bring them inside, and they do go dormant, then by mid may I take them outside. Recently in one of my travels in Bangkok, I saw a bougainvillea with 5 colors on it. It was an incredible sight!

Mine will be coming in soon too. I have made it a bonsai, now in training for about 4 years.