A viable option is to burn them ourselves and return them to the earth. The ideal situation would be to burn the palms by themselves, collect the ashes and bury them in a place that will not be easily disturbed. We do this because blessed palms are a sacramental. These are an ordinary object that has been transformed or elevated to a higher purpose that draws us — through their use — closer to Christ. As such, they should be treated with dignity and respect rather than simply thrown in the trash.
Another option is closely related to the first, but omits a step. Because they are a sacramental and are biodegradable, palms may simply be buried in a place that would not easily be disturbed. In both, the case of the “burn and then bury” method or the simple “bury” method, neither require a deep place of burial. A few inches below the earth, where one can be reasonably assured they will not be disturbed until they return back to the earth from whence they came, is fine.