My basses are pretty stable (no idea why) and I have never known or cared the number of millimeters between the 12th fret and the string. However, my eyeball estimate is around 3mm. This is on my 1973 Rickenbacker, which I have NEVER taken to a shop to have setup in the 24 years I've had it.
I've always played pretty aggressively, so I like a little bit higher action. Now, I don't have to give myself tendonitis to make the bass play, but I have handed my bass to other folks who have a hard time getting the sound out of it that I do -- they usually seem to think I've turned the volume way down on them.
With super low action, I find the bass to be stiff and unresponsive dynamically. Of course, too much fret-clacking makes me back off the right-hand anyway. With too-high action you get a great fat tone, but it takes a lot more work. I have re-shimmed the neck on my Hondo P bass a number of times playing with it -- but I don't think after a certain point action makes much difference. The neck is simply clunky on that bass.
My Squier VM-J basses (one fretted the other fretless) both came off the wall and into my hot little hands with nary a change in action.
I don't like it too high, but I don't really do micro-adjusting of the bass. I have just never had a moment with any of my basses except the Hondo where I thought I needed to change something. And the Hondo I screwed around with after reading a BIlly Sheehan article in the late 1980's that recommended (among other things) "cracking" the neck to break it in. I shimmed and screwed with that neck until it was virtually unplayable, then tore it all out and re-set it the way it was supposed to be . . .still kind of high, but it was playable for me.