What is your definition of bishopric? If you mean the bishop and his counselors, then yes, they all have donation batch approval rights in MLS provided they have been given financial rights in MLS. They all can write checks if they all have signed the signature card. I see no reason a counselor should be denied financial rights in MLS and/or check signing rights. Any counselor who has not signed the signature card should not sign checks until he signs the signature card.
Handbook 1,
14.3, outlines ward financial responsibilities. The responsibilities for the bishopric is covered in
14.3.1.