Quite a number of times I have read the idea of bleeding the air after removing/replacing the radiator cap, (Fu man mentions it all the time) and I always check both the radiator bottle dip stick AND the radiator cap, in fact I top up via the cap (not topped in over 12 months) and I have never ever bled the system after removing/replacing radiator cap, and I have never ever had a problem.
The cap is, if not above the radiator, then certainly level with it, and, as the OP has stated, once the bubbles have gone (air rises/fluid drops) then for all wants and purposes, the system should have no air in it.
If I do top up I do it when the engine is cold or at least not hot/under pressure.
When I replaced the radiator a few years ago, I bled it through the bleeder nipple on the radiator then topped up through the radiator cap.
Just saying.