Well after having several problems myself against a Pit player, there are several things that I'd like to address:
1: Hitting Pit with bair is NOT easy. In fact, this was the attack that I could not seem to land at all. I had much, much better luck with dair.
2: Mirror shield. Can become your biggest enemy with charged shot, so be careful. If you plan on using charged shot at all, you better be unpredictable, and not use it too often.
My counter to Arrows (on the ground) is just small charged shots, and spot dodging. Arrows eventually became not a problem to me.
Super Missiles seem near useless, better stick to homing.
A great combo that I came quite fond of using is if you manage to catch Pit in a dtilt, jump up (don't get caught in his dair PUHLEASE) catch him with a uair, (single jump) follow with a mid-air jump, repeat with another uair, then try to follow up with a screw attack. If you are uncomfortable with falling in the state of helplessness, leave out the screw attack, but it racks up pretty good damage, with his really **** helpful against Pit since he isn't going to fall off the stage.
I was able to air dodge pretty much most of his edge guarding techniques, and screw attack seems to be extremely helpful for battering through any incoming air attacks from above, it seemed to catch him offguard everything, especially since it cuts through all attacks. I'm loving ^B again since the 64 days, I thought it sucked hard in Melee.
I pretty much always grapple through Angel Ring, and If I get caught in it, always DI away from Pit, good god, there's no way you're going to get above him. Sometimes the most useful tactic to preventing it is just by vB, heh, sometimes I could see it coming and would just lay these continuously (like 3 bombs) and it's just a simple annoyance.
That's my advice for now, I'll check back later.
Also, thanks for the zair advice, I didn't even really try too much of that. I'm gonna have to look into it.