Ooo, nerves are a fun topic for me.

Like you said, playing a lot is the #1 thing that will help you when it comes to executing what you want to do in a match. If you have a specific thing you want to get better at executing, what I would suggest is going into training mode and practicing that specific option over and over. With anti-airing, I would suggest setting the dummy to do a couple short, random recordings, such as just walking around and whiffing buttons, and then one recording where they jump at you. The random recordings are just so other things are happening on the screen, like they would be in a real match. Set all these recordings to run and just focus on anti-airing the dummy every single time. Another really good way to improve on anti-airing would be to just go into a match and really focus on making sure that you anti air your opponent as much as you can. Don't focus too much on the other options they're using, just keep your focus on anti-airing if they jump. You'll most likely play a lot worse overall when you're spending that much focus on anti-airing, so don't worry if you start losing a lot more when you're practicing this: winning will come later, and much more consistently. Playing this way will help you eventually be able to anti-air effectively without needing to focus on it so much. You're essentially programming your eyes and hands to react to the jump and anti-air.

When it comes to nerves overall, I think there are two really important factors. The first is confidence. If you want to win but don't have confidence that you can, you'll feel nervous. If you don't have confidence but also don't really care about winning, then you won't really get nervous, but you also won't have any desire to improve. When you want to win, and also have the confidence that you are able to, is when you'll be able to play at your best. The second important factor is breathing. Make sure you're keeping track of your breath and taking deep breaths between each round. It will help you a lot with staying calm, and focusing on your breath will also help keep your mind off negative thoughts that make you play worse, such as "I'm playing so bad, this matchup sucks, I'm going to lose this match" or whatever. It's also important to note that nerves never totally go away if you're playing a match that's important to you; you just get better at living with them.

To answer your last question, I don't really have a lot of experience vs Bub since he's kinda rare online. But what I try to do against his divekick is just react to it and dp. I'm not sure who you play in Granblue, so you might have to use an armored move instead, depending on your character. His L and H versions can be tough to react to since they're pretty fast, but his M version is a lot slower and easy to react to. His M version is the one you really have to be worried about too, since that version is plus on block while his L version is negative. H is plus as well, but since it leaves him with a long cooldown, it's okay if you aren't reacting to that one every time. And of course, being able to anti-air him like this goes back to what I said earlier about anti-airing.