"On your left"

What do you say when you approach another trail user from behind?
According to the politically correct trail monitors, you're supposed to announce yourself with a firm, "On your left."
But I have some problems with that.
First, from my own experiences, that does more harm than good. When I'm quietly and peacefully walking or riding on the trail, and someone comes up behind me and blasts out, "On your left," it (in the words of my college literature professor) "scares the bejasus out of me!" I'd much prefer that people just ride by. Of course that may be because I always stay to the far right and don't feel compelled to take up the entire trail.
And whenever I pass someone and say, "On your left," they either ignore me, get the bejasus scared out of them, or hear the word "left" and move in that direction thereby making matters worse.
So I thought I'd solve that little problem by installing a little bell on my bike and unobtrusively ringing it as I approached a pedestrian or slower bicyclist. (There aren't many of those.)
Well boy was I ever upbraided. About the second person I came to was a lady walking her dog. Upon ringing my bell, she moved to the opposite side of the trail as her dog, held his leash about neck-high and asked, quite sarcastically, "Did you want to go by?" I guess she felt the bell was not an acceptable way of begging her permission to pass her. She wanted me to say the exact magic phrase (perhaps "on your left?") before she could grant access to half of the trail.
So I said, "No! I just ring the bell to see what kind of Pavlovian reaction I would get out of you and your dog."
Okay, so I didn't actually say that, but thought of it about ten minutes later. I never think of good retorts until about ten minutes after the fact and far away from the intended target. I'm a delayed-release smart mouth.
So here's my point: Is there really any good way to pass people on the trail? It seems like no matter what you do, it's wrong about 50% of the time.
Now it's your turn. Let us know what you do when you pass people on the trail. Does it work?

"On your left"