I have a number of overgrown bougainvilleas that were hit by frost damage last season. As such they have a lot of unsightly, dead branches on them. This spring I plan to do a severe pruning, but I'm dreading it. Bougainvillea's have some nasty thorns on them, end even when doing some simple trimming, I'm always covered with scratches, and the toxic nature of the thorns make my skin itch for some time. They are also a royal pain to get into trash bags as they simply shred them if you aren't careful.
What is the best way for dealing with disposing of a lot of bougainvillea branches without looking like I tangled with a pack of angry cats?
 I should clarify. severely pruning back the bougainvillea's will create a lot of very thorny branches, often quite long ones. When I have trimmed the plants in the past, I ended up doing a lot of cutting the branches into smaller, more manageable pieces so that I could shove them into trash bags. I'm not looking so much as to how to keep from getting cut up, although the suggestions are great. I'm really looking for an idea of how to dispose of the branches. How do people that have dealt with a very large amount of these thorny branches deal with them? They don't compost well as they are.
Perhaps could I burn them? I know I can't do that with plants like oleander because of the toxic nature of the smoke, but what about bougainvillea?