The Collaborative International Dictionary of English v.0.48:

Bay State \Bay State\
   Massachusetts, which had been called the Colony of
   Massachusetts Bay; -- a nickname.
   [Webster 1913 Suppl.]

WordNet (r) 3.0 (2006):

Bay State
    n 1: a state in New England; one of the original 13 colonies
         [syn: Massachusetts, Bay State, Old Colony, MA]