Dair is a good move to pressure the opponent when they're on the ground. You can dair and it sets up other options, such as grab or just dair again. I like to dair and mix up to land on one side and grab to throw off the edge. If you can dair and follow their SDI and keep using dair they can slip, which you can follow up with a rest once they're around 80%.
I mostly space with bair though. It's a really good tool to use as a "get the f away from me" tactic or a "oh hey, I can try to combo, stale, and rack up damage" tool. You have to channel your inner hungrybox for this.
Pound on shield is also good since it takes almost half their shield. the Hit box on it lingers and if you can space it where it hits on the last frame, you can mostly get away with it or get away w/ minimal damage. It creates momentum because if the opponents shield is low, they would have to play safer which you can get a little aggressive.
I've also been using more rollout and have been getting good results...only if they try to shield or challenge it. When you rollout, as you aware, you can dictate the path where you're going, but also can choose when it'll hit the opponent. I've been working on timing the rollout when you switch the opposite direction at a certain point, it goes past them, but doesn't hit. It's good to do, especially if they sit in shield and it wears down because it's almost a guaranteed hit and almost a guaranteed kill on most characters if it hits around 90% I don't have much data on this to confirm, but I've been experimenting.
With all that I said, you have to make sure you mix your moves up. You can't be like MK and throw moves because you know they work. The Good lord of Smash didn't grace Jiggs with much priority. If you become readable, the opponent can start baiting you or can power shield. If your pound gets power shielded, it's a sad day. Jiggs character formula is half bait and half reads; you gotta learn both halves to be successful.