Here is a link to an archived Q&A about this topic here on the Site:
http://garden.org/nga/searchqa...
I have only ever had 2 successful rootings of these beauties (I've only tried 4, half isn't too bad, right?
). Some people say it is easy and some find it to be nearly impossible--of course it will vary greatly based upon your climate, the time of year, and the genetics of your specific plant. The two that I had root successfully were from just following basic rooting tips such as, diagonal cut, rooting hormone, etc. as well as the additional tips of:
-Make your cutting about 5 to 9 leaf nodes in length.
-The cutting should be semi-hardwood or semi-ripe
-Knick a leaf node or two that will be submerged in soil to possibly start root growth from them as well, as the old leaf nodes hold a higher percentage of growth hormone than the rest of the cutting.
-Use exceptionally well draining material, as Bougainvillea cuttings are very susceptible to moisture damage and rot.
-Seal in moisture with a ziplock or something similar (by placing it over the small pot)
-Allow it to get a few hours of direct light a day, without allowing it to become too hot or scorched.
Of course since they are slow growing, it can take anywhere between 6 to 12 weeks for roots to grow and become established. They are known to have very finicky and sensitive root systems, so I do not advise any "tug" testing for roots by pulling on the plant or anything similar. Doing so can cause the new cutting to go into shock, which may undo all of your patience and work. With that being said, once it is rooted and you have a couple of sets of new leaves (probably 5 or 6), you can feel free to repot it into a fairly small pot, just be sure to be extremely gentle with the root system when you do.
