It helps to understand what his all of his moves are for. Here's a rough breakdown.
Jab: Basic poke, use it to control space on the ground. The first jab is what you want to use the most, the second jab should be treated like a seperate attack. The full jab combo can lead into tech chase situations at low-mid percents, starting from maybe 11-15 ish percent or so.
Now, you want to avoid using both hits blindly, if you ever want the full combo, it's better to just hold the a button. This way you save frames if the first hit misses.
F-tilt: this is your short hop anti-air, and mid-range zoning tool. It's also a good option for edge guarding and whiff punishing.
When your opponent is short hopping a lot, space this move while angling it up. It's a solid anti-air option vs short hop aerials that use limbs or against the lesser ranged sword users.
Angling it down at the ledge is a good way to punish ledge snapping when dtilt will not K.O, this is good for setting up gimps or just forcing the opponent to take extra damage.
The start up of ftilt leans bowser back, which makes it great for creating whiffs in mid-close range and punishing them. If used in this way, ftilt can technically "outrange" moves which have more actual reach than it does, and it can even beat moves which are faster and should have hit you first, but this isn't a tactic to rely on long term, use it wisely.
Up tilt: This is your full hop anti-air. It's useful against characters like fox that love to abuse full jump and double jump baits. It's also a good landing punisher and a good way to cover multiple options thanks to the large hitbox.
D-tilt: This tilt is a bit more tricky to use well because of the big commitment and the fact that it only covers grounded options. It's pretty useful for catching spot dodges, and in tech chase situations, especially if the opponent rolls into you while getting up. It can also punish ledge snap attempts just like ftilt but is marginally harder to time in exchange for stronger knockback at late percents. Generally, you wont use this one in neutral unless you are trying to catch a spotdodge or wanting to damage or break a shield.
F-air: This is basically an aerial up tilt in that it puts out a big hitbox that can cover multiple options. Most characters can't make it over a short hop forward air without spending a double jump, so it can service well as a full jump anti-air if short hopped and as a solid short hopped air to air if you space it well. Of course, it also hits grounded options unless that option puts your opponent on a low enough profile to get under it. If you hit with it, it can be comboed off of under certain conditons and can set up tech chase opportunities.
B-air: You can use this to hop over projectiles a little easier, you can also toss it out as a retreating poke in situations where you need to give up space. In neutral, I find it excells when used for trades, it wins in most situations and Bowser has the staying power to afford going for a few trades here and there. Note that his legs tuck in before kicking, which can be used much like f-tilt, as mentioned before. It's also a servicable out of shield option if your opponent is behind you, but you may want to use it only on the laggier options or as an occasional mix-up.
Up smash: This is an overall anti-air and an alright out of shield option. The shell invincibility can be used to break shield pressure or for stuffing any aerials coming from directly above you. The second hit can catch people who airdodge the first succesfully, but is weak and not 100% reliable as they can easily land outside of it. Being a smash attack, it's not hard to punish, so don't spam it.
Neutral air: In neutral, it could occasionally be used as a mix-up on shield or surprise shield breaker or shield stab if the shield is low enough on HP. Otherwise, this shouldn't be used often in neutral.
Down b: punish tool, plain and simple, it's a good idean not to try getting too fancy with this, though it does have a few other uses outside of neutral.
Side b: punish and mix up option, plain and simple. From the air it becomes a workable option cover vs standard defensive options like shield, roll, and spotdodge. Try to always land as close to the edge you are facing as possible, but beware accidental SDs. Otherwise, if there are platforms, and it will K.O, land on the higest platform instead.
There's plenty more, but that's a rough look at the basics, experiment with each moves to find what works best for you.
Hope this helps!
