I'm trying to understand tuning a bit better, and my old 450 size quad always flew pretty badly. So I've taken the plunge and upgraded it to BetaFlight 2.9.0, then started working through the tuning guide on their Wiki (https://github.com/betafli…/betaflight/wiki/PID-Tuning-Guide). To date I've either flown stock PIDs or messed with autotune. This is my first attempt to tune something properly from scratch.  I think I've made good progress to date, but before I get lost, I want to know I'm on the right track...

I started with the default settings, and nudged the P gain up bit by bit until I just barely started to see oscillations, then backed off to just over 70%. Then started working I upwards, raising it step by step. I haven't changed D at all yet.

Throughout the whole process it's had some oscillation that seems like bounce back. When I nudge the stick and let it go, it wobbles a little, then settles. As I raised P and I though this has developed into a situation where if I give the stick a good nudge and let go, the oscillations rapidly grow worse until I cut power and disarm because it's pretty much rolled inverted.

If this is bounce back, then the tuning guide says that it could be too much P, or not enough D. Given that my D is still very low, seems like that my next steps would be to raise D til my problem goes away (or it becomes obvious D isn't helping), then finish tuning I. Does that seem like a sensible approach?

If you raise I too high it can give you some very bad results like flying away on you. Best to start I at default and raise it enough that you don't get any drift when you cut the throttle descending straight down. Another test is to fly straight, roll into a slight angle, release the roll stick and continue in the same direction. If it stays locked to where you've aimed it leave I alone til you've moved further in your tune. The basics of P is move it up to get more responsive control and backing off when you start getting oscillations (not necessarily prop wash, that's more for fine tunning) which can be cured with D but that's where it becomes a fine tune and a subtle game between P and D. Do yourself a favor and look through Joshua Bardwell's RC Groups tunning thread and his black box log analysis thread.

thinking about it you might get more right off the bat with his practical tuning vids.

the bounce back you're experiencing could also be stick deflection and not your gains. you said that when you let go of the stick you get a slight bounce then it settles. it could be when you're letting go of the stick the spring is pulling the stick. try to move the stick back and forth with out letting go of the stick.