Since I'm from Tucson, I have also wondered about this. I also miss rosemary shrubs -- and oleander, too, believe it or not. I think it's the scents.

Anyway, I subscribe to the Chicago Tribune, and when you do, you can get a generous number of free back issue searches. Here's what I found on bougainvillea in Chicago, written by Lee Randhava of the Chicago Botanic Garden. It's from a regular Sunday Home section column.
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Bougainvillea is best grown in a container; [Chicagoland Final , NS Edition]

Lee Randhava, Special to the Tribune. Chicago Tribune. Chicago, Ill.: Jan 29, 2006. pg. 6

Q. Is there any way I can grow bougainvillea in this area, either as a houseplant or as a summer annual?

--Lucia Myerson, Chicago

A. Bougainvillea is a woody tropical vine native to dry, hot, sunny areas of Zone 9b to 10. There, bougainvillea blooms for more than six months if planted in well-drained soil. Because the vine is frost-sensitive, its outdoor season in Chicago is restricted from mid-May to mid-October.

Best grown as a container plant, it makes sense to start with as big a specimen as possible to maximize the enjoyment of the summer flowers. It prefers a fast-draining mix of coarse bark, soilless mix and perlite with a weekly application of half-strength balanced or hibiscus fertilizer.

Water only when dry. Before fall frost, move it to a warm, sunny greenhouse, if available. In the average home, it will go semidormant, drop its leaves and stop flowering (or possibly die) because of low light and too cool temperatures. Reduce watering even more and do not fertilize.

If new growth appears in spring, resume normal care but hard prune the plant since it blooms only on new growth. Take the plant outside in mid-May once it has been acclimated to outdoor conditions.

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It seems to me I have seen the plants in garden stores around here in summertime. But if not, maybe we could have one shipped during the warm months. I have some really hot, sunny southwest facing windows that might be warm enough in winter.

Oswegian

I have had a bougainvillea for two years now. When I bring it inside in the fall, immediately all the flowers fall off. It really surprised me the first time. It drops some leaves but then just sort of settles down. I water it about once a week. It gets plenty of sun. Once it is safe to put it outside, I fertilize it. Last summer, it grew and flowered again. I bought it at a local greenhouse and I think I remember seeing them at Home Depot. Hope this helps. --Sophie

I have two bougainvillea plants that my father started from cuttings when visiting us in Italy in 1977. I inherited them when he died in 1984. Since then, I have had great success with them, in SE Pennsylvania, New Orleans, and now, in southern Indiana. I plant them outside during the summer and give them plenty of sunshine and room to develop lush branches and extensive roots. Sometimes they bloom a bit, but their major "bloom" (these are actually bracts, which are a type of leaf--the actual flowers are tiny, white, and not showy at all)has always been during the winter--at least for me. I have read theat sunshine is the key ingredient in getting them to flower, and that they can flower all year round with proper light.

I pot them up in fall, prune the branches way back (mostly to keep them of a manageable size), and put them in the sunniest window in the house, which has a southern exposure. They drop most of their leaves and go dormant briefly, but soon grow out and are covered with the gorgeous pink bracts for most of the winter. Good luck with yours!