bryon i think i can help you a lot vs jigglypuff.
overall, you don't have to force yourself to get damage on her. this is how i think of it: she will rack up damage if she spaces poorly. you were making the right move choices, like fair, nair, and pk fire, but you were rushing in with them almost the whole time.
since she's a very aerial character, a good strategy is actually to stay on the ground. short hop fairs in place or fading away can keep her out. like i mentioned before against marth, shielding is pretty ok because her main goal is to space aerials at the tip. and her grab game is much worse than marth's.
before you can confidently go in, you gotta watch her movement patterns. some puffs like to go directly toward you and attack, and some puffs like to use long-duration aerials above you to prevent you from jumping. there are different ways to deal with both. if she is attacking you directly, you can space her out with fairs and pk fire. if she hits your shield at the tip of her aerial and fades away, you can sometimes punish her with wavedash forward fair or even fsmash. even if you can't punish (which means she spaced it well) at least you can gain some ground and not be pushed into the corner by wavedashing forward out of shield. if she hits your shield too deep, dair out of shield might end up doing more damage than shield grabbing, since it can sometimes combo into itself, or lead into pk fires when she rolls. it's better to keep her point blank rather than allowing her to space.
if she spaces aerials above you, you can run beneath her and either try to attack from beneath/behind her, or just regain center stage. puff's goal (besides resting) is to push us to the corner with sheer spacing, and then get easy edgeguards. so defending center stage is very important.
if her spacing game is just super good, one good strategy, like i always mention, is run up shield haha. this could cause her aerial to be too deep and you can punish out of shield. of course she can counter this by grabbing, but she gets absolutely nothing after the throw against ness, except positioning i guess
overall, attacking her is too hard, and not good, because all she is doing the entire match is spacing and her aerial movement is better than any other character's. so really we just have to defend ourselves from her obnoxiousness.
never forget:
source: lots of exp vs puff in melee. she's my best matchup. haven't played the matchup too much in PM yet but i'm guessing it's largely the same
edit: not saying you can NEVER EVER approach... once you know her movement well, you can find times to weave in. it just really depends on her patterns. cuz when i watch hbox, his spacing is so good, and unpredictable, that he looks unapproachable
which is why he only loses to fox lol...