Bishop was trying to become the fifth NHL goalie to get a shutout in four consecutive games he played since 1929-30, when the League implemented forward passes in all three zones.
"I think he's being smart," Montgomery said. "He's trying to make sure it doesn't become a two-week thing."
The Stars, who were tied with the St. Louis Blues for third in the Central Division, have 11 games remaining.
Dallas recalled goalie Landon Bow from Texas of the American Hockey League to back up Anton Khudobin against the Vegas Golden Knights on Friday. Bishop (24-14-2) missed his 12th game because of injury this season. In the previous 11, with Khudobin starting, Dallas was 3-6-2.
Khudobin (13-14-3) has a 2.55 GAA and .924 save percentage. Dallas has a team GAA of 2.47, second in the NHL to the New York Islanders (2.34).
The other NHL goalies with at least four straight shutouts since 1929-30 were Brian Boucher of the Phoenix Coyotes (five games, Dec. 31, 2003-Jan. 9, 2004), Roy Worters of the New York Americans (Nov. 12-20, 1930), Charlie Gardiner of the Chicago Blackhawks (Jan. 8-15, 1931) and Bill Durnan of the Montreal Canadiens (Feb. 26-March 6, 1949).