What's wrong with my car?

[Undertoad]

Inspired by Carr's thread "What's wrong with my lawnmower", and by all y'all.

What I have is a noise. This noise is around and about the right front. It matches the speed of the tire. At highway speeds it is fast enough to be a buzz. It doesn't get louder or software at speeds, it remains the same volume. And it's a light volume, unless I'm driving next to a building where it reflects back at me. It's an almost ignorable volume.

It is not a "click" noise. In my history I have had several things embed in my sticky tires; nails, screws, someone's bent key... these all make a click every time the tire goes round. This sounds more like I'm running over something soft.

But the noise is not there all the time. Hard to say when it's happening and not happening. Today, I think I noticed that it started after a swift right turn, and seemed to stop after a left, but it's so intermittent that it's hard to make a reliable guess out of it.

I tried to rule out wheel bearings by jacking the car up and trying to wobble the wheel across its vertical axis. There's a Youtube that shows how to do this. The wheel felt solid.

I thought it was happening when the tires got warmed up, so I took it to a tire place. The owner of the place drove it around for five minutes and of course, the noise never happened. The noise was happening on the way in, stopped happening while he drove it, and started up again ten minutes after driving out of the place!

But the dude said the tires should be warmed up enough to show it and otherwise, they felt completely smooth and fine to him. It's true, I don't believe this noise ever becomes something I feel, when I'm driving down the road.

So now I'm angry, confused, and humiliated, except that I'm not angry. And I know I should do what any sane, rational person would do, which is to turn the stereo up and ignore the problem until it becomes something that makes a much louder noise and/or vibrations, making it easy to diagnose and list a price for.