Get off of platforms as soon as you can against Jigglypuff. He's too good at juggling you--you always want to position yourself below Jiggs if possible.
I wouldn't dair at all against Jiggs. One whiff, and you get Rested.
In general, don't spotdodge as Bowser. At the beginning of the match, Jiggs sharks you, and you spotdodge. Fortress OoS is much better here because it damages Jiggs and sends him upwards, which is where you want him to be.
Don't uptilt a small character when he's right in front of you on the ground. That won't hit. Reverse uptilt will, though.
You could have fair'd during that Wall of Pain instead of take it and Fortress to the stage like you did. You should never Fortress from above the stage to return to it against Jiggs--that's a free Rest.
I lol'd at the jab KO.
In general, you fished for grabs a lot during this match. While GR > upair is amazing in this MU, it's not the sole reason this is an easy MU for Bowser. You can literally just get the lead, walk to the middle of the stage, and stand there. Don't forget that up-angled ftilt is great for stopping aerial approaches, and Fortress OoS beats Jiggs's dair.
Bottom line: Try to trade hits as much with Jiggs as you can, because eventually he just can't take it. That said, be wary of hitting back when you're being hit offstage. Good Jiggs mains bait fair/nair and punish with their own aerials offstage.
NEVER do ledgehopped Fortress against Jiggs. Is it completely random and unpredictable? Heck yes. But it can and most likely will (although it didn't here) get you punished with Rest.
Your biggest problem here is whenever Jiggs got close to you and you brought up your shield, you stood there for about a second or so before going for a grab. You need to react quicker than that. Don't always fish for the grab, as Jiggs players are ALWAYS expecting that. Fortress is generally a safe bet--just don't always Fortress OoS against Jiggs because good players will bait it and punish with Rest.
I see you like jabbing a lot. I can dig that. Don't forget that you can jab cancel into other attacks, including reverse attacks. There were a few times I noticed you jabbed the opposite direction of Jiggs only to continue the jab and get punished. A lot of times people won't expect a reverse ftilt or pivot grab out of a "mispredicted" jab. Sometimes I even jab the wrong way on purpose just so my opponent thinks I'm open for punishing, only to take a knuckle in the face.
I'm generally very grounded against Jigglypuff, but don't forget to throw in some Klaw Hop mixups every now and then. It's gonna be fresh if you're playing grounded, which leads to some early KOs against light characters like Jiggs.
Back to jabs real quick: If you're looking for a grab, a lot of times people aren't expecting jab > grab. Limit told me he does it more often against light characters--Jiggs is a prime example.
Hope this all helps, man. Sorry for the rather random order--just jotted down my thoughts as they hit me. Feel free to post more videos when you've got them.