Yes you can. I've used shed bamboo leaves as bedding for one pen that happens to be right next to a bamboo clump. It worked great.
Whole side springs or cut bamboo with green leaves still on are great for them too- they like to pick on and pull apart the green leaves. They won't eat the dried leaves.
p.s. what varieties did you find to do well in the desert? I've tried several.. most struggled with the summer time temps(110-120F) and so needed TONS of water to just survive. Down to just one clump of unidentified clumping style, looks like some type of timber(solid green culms are getting thick). If your bamboo really turns out to be arundo(stem has single long leaf alternating on each side, like corn), that's actually a reed.. although everybody calls it bamboo. I'd say arundo leaves are too rough and sharp edged to use as bedding.. their leaves give you countless paper cuts, ouch...
