@Holy SoldierWell, everyone was kinda supposed to hear Peach's scream. And it wouldn't make sense for Mario to not hear her scream, since Bonnie was at the same location and heard it.
I think you're overestimating the distance between Mario and the castle. If you look at the Paper Mario layout of Toad Town, you'd see that the western entrance and the castle aren't that far apart. I know Bowser used a vehicle, but keep in mind that it was never specified where Bowser was and how far he was from the castle.
If I was in your situation, I'd follow Bonnie who is clearing the way to have an easier time to get there quickly. But really, you can do what you want. I'd assume Mario would run into Bowser and be briefed on the situation later anyway. I hope I helped ya decide on what to do here :P
I kinda intended for
@Lugia's char Blake to fight Fire Man, but really anyone can take him on. Either way, he should probably be stopped considering he's rampaging around town :P