Given that this is a bush, the obvious expectation would be that this could be out in a composter as waste organic matter to convert into bone meal, as is the case with a vast number of other plant blocks and items. This, however, is not the case, and the composter completely refuses to acknowledge dead bushes as any sort of valid input.
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To the extent that information on minecraft.net is "official", we have this Block of the Month article on the composter, which says that dead bushes cannot be composted because they are "too dead". Therefore, this ticket should be closed as "Works as intended."
I always found it nonsenical that things containing bones (fish, steak, mutton, and bones themselves) cannot be converted to bone meal in a composter, but that article unquivocally says that they cannot.
Can confirm