How does "generic" pressure work?

I have only been playing the game since mid Nov and went through a few characters, and only started finding success and have fun playing bryan. Got him to Brawler/Marauder and think it is good enough for now and wanted to play someone new and I picked up King. Problem with that is I think my mentality about pressure is very skewed because I got decently far with Bryan only. Here is how I pressure with Bryan:

Start with 1, 2, 3, play dick jab to check pressing, if not wait for my turn, if yes, try to go for big move on +6

On my turn or at neutral, jab into b+1 or qcb+3, get plus frames, and df+2, 1 or df+1,1,..,2 to check mash. If they don't mash, either keep up with b+1 or qcb+3 and play a 50/50 kind of game on whether they have to block low or mid.

Ofc this is not the only thing I do, but regarding pressure, I get pretty far with this (I think for first fighting game and 2 months of playing semi consistently its pretty far). Problem with King for me is I don't have moves that are +4 or +5 that I can throw out in neutral, or that has a good chance of doing damage (qcb+3 on bryan) so the most I can get is +1 (1 jab on block or d+3) or +3 (f+1+4), and I kind of just get hit when I try to get bigger moves with such small frame advantages. Sometimes if they press then I can fish for b+1, but if not I just kind of spam + moves but do no damage. So what should I do when I have small frame advantages but the opponent isn't really pressing?