I happen to live where bougainvillea grow freely in landscape and I have to say... I kinda don't like them
Let's face it, they are a thorny vine that, with constant attention, you can beat into a thorny hedge. Perhaps I wouldn't feel this way if I wasn't constantly battling with them (they will throw 8-12' thorny runners in all directions if you let them).
Yes they can look beautiful if you trim them at the right time, and get all of the branch tips to push bracts all at once. But to do this, you have to trim the long runners before they become long runners, so that they will develop fine ramification. And if you don't have hot conditions with lots of direct sun they will pout and throw leggy growth. They don't even like partial shade down here. I have a bush next to my koi pond that gets a little shade from a Canary date palm... and though it grows I never get any color from it. I personally think trying to grow a bougainvillea bonsai in anything other than perfect tropical conditions would be an exercise in futility.
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Let me edit this to say... rather than "I don't like them" I think you can find many other flowering / colorful bonsai that you can keep in your setting that will cause you less grief, and give you more pleasure.
If you want flowers, go for Japanese azaleas or Chinese quince. If you want fruit... and want to travel down the rabbit hole... go for the holy grail.... princess persimmon
You could probably also keep golden bean kumquat.