I hold .0005 total tolerance on bores all the time on lathes - most of our work is exactly that; a bore that's roughly 4-5x diameters long, and the diameter is +.0005/-.0000. Part runs anywhere from 20 parts to 400.
Set a tenth reading bore gauge. Job done. There really isn't anything to it, you just have to check each part and get an idea of where the machine is going to be on the next part.
The first part should come out right; sneaking up on a bore is a simple matter. Each time you take a pass on your setup part where you've changed the diameter, you need to make a skim pass before you change the diameter again. Sneaking up on stainless is relatively easy; it's aluminum that's difficult.
So you have your first part, but the next part is still going to come out wrong. Note how far out it is, -.0007 or something. Write it down. Now sneak up on the diameter again. It'll take less than .0007 to get there; after you've finished sneaking up, add enough offset to make up the .0007 measurement. Say it was .0007" out, but between spring passes and adjusting offsets, you only needed to move the machine .0004". Move it another .0003" - the next part should be dead on.
Also, in the morning, I don't bother warming machines up. I note where the machine was, size wise, the last part of the day. Next morning, I bump the offset down .001-.002. Run the part. It'll be a little bigger or smaller; I write this number down, and every morning thereafter all I have to do is enter the difference between the expected and actual I got that first day. I figure I have to babysit the machine anyway, so might as well not waste time warming things up.