Pep Guardiola's men cruised to a 4-0 win at Hannover on Sunday thanks to two goals from Thomas Muller and one each from Mario Mandzukic and Thiago Alcantara.
The win restored Bayern's 19-point advantage over Bayer Leverkusen at the top of the Bundesliga, with a 24th league title almost guaranteed.
On Wednesday they defeated Arsenal 2-0 at the Emirates Stadium in their Champions League last 16 first leg, meaning they are in a strong position in each competition and Schweinsteiger is hoping to succeed on both fronts after returning from an ankle injury.
He said: "It's great to be back. I feel good and it's great to come through 70 minutes unscathed.
"The Bayern training sessions are high quality, but I've got to use these minutes. I'm not getting any younger, but with my ankle injury games like this are crucial.
"Pep gave me a lot of encouragement, but I've got to be top fit in order to help the team.
"Our priority is the Bundesliga and becoming the first team to defend the Champions League.”
Guardiola singled out back-up goalkeeper Tom Starke, whom he gave a first Bundesliga appearance of the season to on Sunday, adding that he was happy to give him a start and content with the 32-year-old’s performance.
"Tom Starke deserved a start today," Guardiola said. "It's just difficult for him being behind the best in the world (Manuel Neuer).
"But I was delighted to give him a chance and I was pleased with his performance today.
"My players executed the game plan and we managed to take the chance to extend our lead at the top."
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