That's how I do it too. I'll tap bell once (and let the ring sustain) when I'm about ~5 seconds from overtaking them so people know there's something coming up behind them, and the sustained sound tells them how fast it's coming. This is especially important with runners, who are prone to suddenly take a U-turn if they're at the end of their route.

Pedestrians regularly wave acknowledgement or even say "thank you." Some other cyclists (especially on e-bikes) just blast by with no warning.

The problem with bells is that they aren't very directional. It's hard for my brain to figure out from which direction the sound is coming from. Someone speaking "on your left" is much more directional, and it includes important context as to what the warning is about.