Cane is a grass, not wood. It will eventually dry out enough to split lengthwise, unless you can soak it in oil to fill the pores well. You can " coat " the outside of bamboo, but it won't allow you to stain it, or soak up oil finishes. Use a varnish, or shellac that is thinned with alcohol.
I would suggest using some tightly woven string, like fishing line, ( not the synthetics) to wrap the end of the piece of bamboo. It the cut is more than 3 inches from the the knuckle of the bamboo, then consider wrapping it tightly in two places. Put some varnish or finish, or even glue on the string wrap to lock the wraps in place. Leave the measures hang somewhere its warm and moist as opposed to cool and dry. The few bamboo fishing poles I ever owned never seemed to survive the dry winters in N. Illinois when I was growing up, without developing splits in the bamboo.