There are many different varieties of bougainvillea, some which grow bushy and others that seem to trail. Yours looks like the trailing variety and really should be potted up slighty, and it wouldn't harm it to have the growing top nipped out so as to make it a little more bushy. I have a friend who lives in sardinia and obviously it grows quite readily there out doors, I adore this plant and have looked into growing it here but unfortunately it doesn't like temperatures below 10 degrees so keep it nice and warm. Dont be alarmed if it looses it leaves in winter though and don't over water it. Hopefully you will be able to keep it overwintered and place it out doors next year in a sunny spot. As for supporting it, any cane that will support the plants weight- good luck