I don't like Paper Mario that much, I just think Paper Bowser looks awesome =D
And as for Bowser tips:
Since you main MK you shouldn't have problem using Up B out of shield, but in case you do, practice it, because it's a VERY important part of Bowser's defensive game. Whenever someone hits your shield from whichever angle, Fortress them in the face, unless their attack pushes you out of range (sourspotted Fortress is nearly useless).
Also use Side B a lot. It quick and deals good damage. It can also be used for "Koopa Hopping" which gives you a lot of mobility, especially if you fast fall between jumps (which is a little hard though).
Since Side B grab has amazing range in the air, Koopa Hopping also sets you up for a quick grab if opponent gets too close.
Fsmash is hella good, so use it whenever you get the chance BUT MAKE SURE YOU HIT. You have to use it wisely, but if you go into a friendly match for training and try to look for Fsmash opportunities, you might be surprised at how many Fsmashes you actually hit with
Play defensively. Don't approach unless you have to. Against projectile users you'll have to pick a stage with multiple options for you to approach.
Learn Bowser's grab release options (specifically, memorize everything you can do to each character after a grab release). Bowser should rarely actually throw his opponent.
Jab cancel. On most characters you shouldn't follow through with your second jab because there are so many better things to follow up with (Marth being one of the possible exceptions.
Lastly, go to the Bowser boards. The guys over there may be a silly bunch, but they know stuff about Bowser so listen to them