Stop Playback and resume at the start of the next bar

MuseScore will start playback from exactly where it stopped if you just toggle the space bar. (Let's call that the space key to avoid confusion with bars of music). If you hit the space key at the end of the bar, when you hit the space key again, Musescore should start again at the start of the next bar. However, you have to be pretty accurate with the timing of the stop.

As you are synchronising with dialogue, I assume that the restart is not extremely time critical. A half second or so delay would not be too obtrusive. Therefore, to give yourself a bit more leeway perhaps you can insert an empty bar between the end of one section of music and the start of the next. You can adjust the length of the bar from the right click menu in bar properties. For example you might have a section in 4/4 and insert a 1/4 bar immediately after it. You can hit the space key to stop the playback any time during that empty 1/4 bar. Musescore will start where it left off with a maximum delay of the full 1/4 bar.

(If you are using US localisation, for bar (musical) read measure.)

If you add a section break, playback pauses automatically - for a fixed amount of time (set in the Inspector), and then it resumes, so you would still need to hit Space to get it to wait for you. But then, Space again starts immediately on the next measure. So I'd use section breaks for this, perhaps st to a longer than usual default pause to give you time a little more time to hit Space to stop it for real.