I have stayed in a good number of county, state, NPS and U.S.F.S. campgrounds. I have never stayed in one that allows you to collect and burn anything but dead and downed wood.

Yes. Bury it, and not near a water soucre. For digging, it's called a plastic trowel:

http://www.campmor.com/outdoor/gear/Product___86702

2 oz. $2.99.