Answer: Bougainvillea blooms cyclically based on day length, so you should see bloom periods basically in early summer and again in the early fall, assuming the plant is receiving enough light and has enough nutrients. They bloom on the new growth, so you see an alternating growth spurt of a couple of weeks, and then a bloom period on that new growth. (If you need to prune it for size, do so right after a bloom period.)
Sun is often the limiting factor as this is a tropical plant that craves heat and sun. Many gardeners set it outside for the summer so it can soak up the sun. In your sunroom, set it so it receives south and west light as these are the more intense.
I have not seen big concerns about pH sensitivity with this plant, it is fairly tolerant of many soils as long as they are well drained but if your water is so alkaline you could try to adjust for that and see if it helps. Of more concern might be the amount and content of fertilizer. You could use a complete water soluble fertilizer with minors such as 10-10-10 plus minors (use less in winter when growth naturally slows) alternating the normal formula with the formula for acid loving plants if you are concerned about pH. Or, you could use rain water.
Overfertilizing with nitrogen can cause excess leafy growth at the expense of blooms, so follow the label directions. It is possible, if you are fertilizing generously and regularly and it is not subjected to the leaching action of rain outside, that it was initially overfertilized -- this can happen when the grower or retailer adds a slow release fertilizer and then you fertilize generously on top of that. (By now, any slow release should be used up.) I thought I should mention this because when you describe it as looking healthy, I hope it is not overly lush due to overfeeding.
Kumquat needs ample sun and warm temperatures during the summer, and rests a bit during the winter. It is a little different from most citrus in that it rests a little longer so can be slow to come out into active growth in the spring. It also resents being pot bound and will stop blooming if allowed to become crowded in the container. I suspect that your plant needs more strong direct sun in the summer and possibly also more fertilizing during the growth period. I would also check if it needs repotting (do this in the spring).
Here are some general container care recommendations for citrus which should help you evaluate your own care routine. Keep in mind it was written for Texas gardeners, so full sun in TX would be intense!
I hope this helps.
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