This is a great discussion. I regularly ride on the Hudson River MUP in NYC, which Wikipedia claims is the most heavily used bikeway in the USA, and it certainly does see a lot of traffic! It's a beautiful way to have a car-free ride, run, or walk with terrific water views and as such draws heavy crowds (especially on weekends) of runners, bicyclists, strollers, etc. So I encounter passing issues regularly.

The technique I've evolved in more crowded parts is to give pedestrians and joggers the right of way whenever possible and to pass when safe without disturbing them. For this technique, I rely on heavy observation. If there is plenty of room to pass people, then I do so slowly and with a wide berth. I only ring my bell and say something when they are completely blocking the route or I observe them weaving back and forth across the path or they look like they are about to cross the path (because they were taking a picture on one side) or there are children present (since they are likely to wander or run all over the place with no warning--more a signal for their minders, actually).

For fellow cyclists, I also pass without signaling if there is plenty of room to do so; if it's a tighter situation that requires the cyclist to move over so I can pass, then I ring the bell and say something.

I think this is a courteous approach and seems to work for me.

I like the idea another poster shared of including a greeting when passing, such as "Good morning!" Makes it feel less like I'm surreptitiously saying, "Get out of my way!" I'll have to try it!