Score Bologna with diagonal lines about 1/4 inch deep.
Anchor on spit, attach to grill. (Place foil drip pan below, if your barbecue does not have a built in drip catcher.)
Cook on rotisserie with hood down over medium coals for 1 1/4 hours or till heated through and browned.
Meanwhile, combine remaining ingredients for sauce; brush on Bologna frequently the last 15 minutes of cooking.
Slice meat about 1/4 inch thick; serve between toasted hamburger buns, with remaining sauce heated and spooned over.