Depending on their dash dance spacing, flame cancelling can often catch any grounded approaches Marth makes. I'll often act like a scrubby Bowser and do doublejump baits in neutral to make Marth think I'll land with a Fair or something. Instead, I'll land with a flame cancel if he starts running towards me to punish. Obviously, this will only work a few times against good players. To avoid this, Marths will usually do one of two things: start catching your descent with an aerial or an Utilt, or dash farther away to avoid the flames altogether. Falling with Nair trades with any hitbox that Marth can put out and will often put us at a frame or positional advantage. If Marth dashes away, you can just do an empty land and take the stage control he gave up. Either way, we win the exchange if we react correctly. However, good Marths will also bait us into falling with a Nair by running up and shielding under us instead of throwing out a move. This becomes somewhat of a 50/50 between Bowser using Nair to beat the sword and using flame cancel to beat the shield. I'd argue that we often have enough time to react correctly to the option Marth chooses, so exchanges like this should usually end in Bowser's favor. This somewhat scrubby option in neutral does rely on Marth actually approaching, so it will only work if you're ahead by percent or stocks.
If you're behind or you don't like leaving the ground, there are more approach options Bowser has against a patient Marth. Crouching and/or crawling in neutral, especially at low percents, is fairly safe against Marth since his hitboxes are generally not strong enough to break the armor. The only exceptions may be his Dair and tipper Fsmash, the former of which most likely actually puts Bowser at a frame advantage due to the long endlag. Marth should only get away with throwing out Fsmashes in neutral once or twice; they should be avoided, shielded, or dash attacked if he does them too often. If Marth does hit you while you're crouching/crawling with sufficient armor, dash attack is usually the best punish. Once Marth is in the air, wait out his doublejump and his sideB stall, then juggle him relentlessly with Fairs or Nairs until he's offstage. All of this was assuming Marth approaches with a hitbox instead of a grab, which is unlikely in this matchup.
If Marth primarily approaches with grabs, as he should, Jab1 is Bowser's best move to keep him out. Jab1 is our safest move in neutral, and we should abuse it. It outranges Marth's grab, comes out on Frame 5, and has about 13 frames of endlag. It can also link into more Jab1's by crouching to cancel the window for Jab2, then attacking again. The best way to do this is with C-Stick Attack. Marth, even with his incredible dash dance and grab range, has a difficult time punishing Bowser's Jab1 in neutral. If Marth still refuses to approach, our general tactic is to slowly and safely take stage control until Marth is forced to react. This is best done by crawling since we have armor while advancing, and we can also use Jab1 immediately from crouch (using C-Stick Attack). Marth will be forced to approach as we take more and more stage control, and we can react to all of his options as described above, assuming you maintain proper spacing. Try to determine when your opponent begins to feel uncomfortable with the amount of space he has to dash dance, then prepare to react to or read his approach. If you react correctly, you should be set up for a combo or string that either racks up percent or sends him offstage.
I hope this was helpful as a somewhat in-depth analysis of our options in neutral against Marth. You can and should use a combination of the options I've described in each paragraph depending on what your opponent is doing. This analysis also applies to similar, dash-dance heavy matchups (e.g. Roy). Perhaps the most important skill or gameplay style we should learn from and apply to this matchup is patience. Bowser has no need to approach in the conventional way (aerials, dash-dancing) since we thrive off of trades and correctly reacting to the approach option our opponent chooses. All in all, we should not use any moves (except Jab1, sparingly) until our opponent uses one, especially against Marth.
