Answer: This plant resents change, so you'll need to be patient with it. It is very drought tolerant and prefers its soil somewhat on the dry side, so I would expect it to eventually recover from not being watered at all. It is a cyclical bloomer so it may rest and take a while for it to begin blooming again, but all is not lost.
Do not repot it now, if it needs repotting wait and do that in the spring. It needs just a relatively small container and should only be repotted if truly cramped because the root disturbance from repotting is a stress on the plant. The time to repot is in the spring. Go up just a single pot size, not too much larger. Use a potting mix that drains freely, try to find something with a similar texture to what it is in now; most good quality container mixes should be fine although I would not use one with a water holding polymer in it. I would not use a self watering container. Definitely use a container with a drainage hole(s) in the bottom. Never leave it sitting in a saucer of water as excess moisture at the roots can kill it.
Set the plant in a spot that receives as much sun as possible. Water thorougly now to re-wet the soil (if you haven't already), making sure the water soaks into the whole rootball. Then water as needed when the top inch of soil has dried out. The plant usually needs more water in summer when it is outside and actively growing than it does in winter. In winter it can handle a cooler room temperature and needs very little water as it basically will rest due to the shorter days.
In late winter, prune it back to control the size and encourage branching and blooming. Once it begins to grow vigorously, increase the water proportionately and fertilize regularly. From spring to fall when it is actively growing use a water soluble fertilizer such as 10-10-10 with minors per the label instructions.
This fall, if your plant is still outdoors now, be careful not to let it get colder than about 55 degrees if you want to try to keep it blooming indoors this winter. Keep in a room with temperatures at about 70 degrees and as bright as possible -- a greenhouse is ideal. If you aren't concerned about it blooming indoors and just want to keep it alive and plan on letting it rest, allow it to chill a bit more, say to 50 degrees before you bring it inside. Keep it in a cooler room, say at 55 to 60 degrees until spring.
Here is a good summary of bougainvillea care you may find helpful. Good luck with your plant!
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