The Bavarians have missed out on major silverware for the last two seasons, but the midfielder is hopeful that they will be able to end that spell this time around
The Bavarians were in fine form for the first half of the campaign, and went into the winter break with a nine-point lead over second-placed Bayer Leverkusen.
"There's a long way to go before the trophies are handed out," he told the club's official website.
"Every man on the team must try and shift up another gear compared to the first half of the season, to work better and with even more focus. If so, we might end up with something this time.
"We defended very well, and that was the decisive factor. It's definitely a change compared to last season, something I particularly notice playing in the centre of the park.
"That's why we're in such a good position. Also the new signing have settled well. It's important we start well by beating Furth and Stuttgart. We need to be up and running straightaway."
Reigning champions Borussia Dortmund are currently 12 points off the pace in the Bundesliga, but Schweinsteiger is certain that they, along with Leverkusen, cannot be underestimated going into the second half of the season.
"Just like us, Dortmund have top quality in their squad. But we mustn't underestimate Leverkusen. They're more defensive this season, preferring to counter-attack using their quick wide men.
"That makes them very, very good. But I still believe it's entirely up to us whether we win trophies or not. We have only ourselves to blame for it not working out last year. Once again, it's in our own hands now."
Javi Martinez's €40 million [£32.5m] transfer in the summer broke a German national record, and Schweinsteiger is happy with the number of options Bayern have in midfield.
"It's great. Javi has fitted in really well. But don't forget Luiz Gustavo and Anatoliy Tymoshchuk," he added.
"Both turned in terrific performances when they played. The coach has excellent options, and that's incredibly important."
The 28-year-old has enjoyed a prolific campaign in front of goal, notching six goals in all competitions, and although he recognises that scoring is not his main duty, he is disappointed not to have found the net more often.
"I'd like to have scored a couple more goals actually, because I had a few chances. But whatever, it's obviously not my main job. Overall, I'm very satisfied."