I'd cut the live stuff. look for culms that are straight as a pipe and with as great of node spacing as you can find. straighter is probably more important than node spacing. 3" diameter cane will make a bow backing. less than that, and you will be cutting it close. 4" is better still. 4" can yield 6 pieces of backing. your mileage may vary. also, the wall thickness of the culms will have some bearing the diameter you can make backing from. thicker walls better.
cut your culm(s), split by hand into however many backing pieces you can get and let it dry indoors for a week or two, then put it outside in the sun. will stay green for a very long time if you don't put in the sun. after a couple of a month or two of drying in the sun, I'd suggest force drying (as in your hotbox at 70-80 degrees with ventilation for a couple of months) it to get it completely dry.
I'm no expert at handling green bamboo culms, but this is what I did last spring with some large diameter cane that was grown here in the USA, and it worked very well. just finished my first litter of bows backed with my new bamboo, and I'm very pleased with the results. was kinda fun handling the bamboo from live culms to a finished bow, and I know exactly what I got and how it was handled and dried from start to finish. sure wish we could grow cane that big this far north. at least we have osage. :D
do not heat treat bamboo for backing material, but make sure is thoroughly dry.