It may not have been a bee but instead was a wasp.  The cicada killer,
Sphecius speciosus, is 1 to 2 inches long, nests in holes in lawns, and
males patrol territories over females' nesting areas (= buzzing about
the nest opening).  Large individuals are the largest solitary wasps in
eastern North America.  They are widespread throughout the east and midwest.
I've gotten several telephone inquiries of the same general sort, and all
have been cicada killers.  They are fun to observe and completely nonaggressive
 
Cheers,
Jim Hunt