I'm no expert with this but have had some luck of late, mostly by way of trial and error. While I may not be following the rules I will offer these tips. Keep in mind I am in a cold climate and your location could dictate other techniques.
My bougies are kept outdoors throughout the warmer months (May-Sep) where they are protected from wind and heavy rain, getting about 4-5 hours of full sun and 3-4 more of filtered sun. When they come in they go onto a wire rack with a small hydroponic light fixture, nothing fancy, roughly 6 inches below the bulbs.
Here's what I think is the important part - this 'readjustment' period of moving from outdoors to indoors seems to send them into an unhappy mood. Over the next several weeks they will mope and look sickly and drop leaves. (this is their Autumn - their deciduous transition). So I let them rest. I take them away from the light stand and move them to a cool dimly lit corner of the cellar floor and leave them alone for a few weeks. This is in Jan-Feb. During this time I moisten them only once a week but no heavy watering. They are nearly dormant.
Around mid Feb. I bring them back up to the light stand which is placed in a sunny corner and let them 'SPRING' - back to life gradually as the sun and the artificial lighting combine to rejuvenate the life cycle. They often look like crap at this time. I sometimes think they have died. But they respond to this very well. I now water them well. As the first buds form I begin the water and fertilizer routine. By Mar-April they are well on their way and anxious to get back outdoors - but they can not be frosted!
This may not work for everyone, in every location, but it works for me here. I would like to hear from LUCENDA in Chicago and get her advice and experience as well as others who do bougainvillea bonsai successfully. Let's make this a bougie primer column and maybe help some who struggle with theirs - perhaps by trying too hard or by misconceptions.