I guess its as hot as if you or neighbors dog would decide to sprinkle some urine on your bamboo.
In high concentrations urine is going to burn roots, especially with plants that were not completely established yet. I think an inch or two thick layer of rabbit manure, even if it contains urine, mixed with some mulch (wood shavings, straw, pine bark, peat moss ...) shouldn't present a problem. If bamboo is still young, you can start with smaller amounts and then re-apply after a while.
PS: I thing dogs love to pee on my bamboo, which got kind of oily patches on lower leaves several times this year when there was no rain. The branches that were "hit" the most, lost most of the leaves, but there are dozens of branches emerging, which means there was only minimal damage. Bamboo grows normally despite being "watered" on regular basis.
