Bishop's performance tied a club record for the most saves in a home victory for Ottawa, which racked up a fifth straight win and pulled into a second-place tie in the Northeast Division, two points behind the Canadiens.
Dave Dziurzynski netted the Senators' regulation goal in the first period.
Andrei Markov scored and Price finished with 23 stops for Montreal, which fell for the second time in three games.
Pistorius testifies he didn't consciously pull trigger when he shot girlfriend
Pregnant Mila Kunis wins 'Best Villain' at MTV Movie Awards