Don't panic. I am amused by the vast numbers of people who have barely cut metal (which you might or might not be ), who think that their machines have to be perfect in order to get acceptable results. It ain't so
Holding a tolerance does not have a lot to do with the bed being twisted. You can compensate for any constant error in your program, but a true lack of holding tolerance is a random error tossed into the mix.
Now, if the linear ways were somehow loose, that could cause them to shift unpredictably from one part to the next.
I never swear by the machinist's level only. The final adjustments always come from trial cuts, and tweaking a support pad (screw) here or there. Although the machine is supposed to have been levelled or sitting flat on a table when it was machined at the factory, you'd never know if your particular casting had a little bit of spring to it which the machinist 'let go' and clamped it down anyway, and cut it. That's just the roll of the dice. Or, the casting may truly have sprung a little after aging some more.
Now if your machine is a one piece casting, and won't sag on its own, then you'll need to lag it to the floor so you can pull down the high corner.
Most of the time, you won't be turning long straight cylinders anyway, so the maximum error condition will be the diametral difference over the length of a given journal length. The widest fit of most components that ride on a shaft would be maybe 3 or 4 inches. Your lathe, as is, has a taper error of .0001/inch. Trust me, there are a zillion other reasons why that ain't going to matter. Some of those reasons are deflection of the stock, eccentric centerholes and uneven heating of the work and toolholder during the cut.
For the final setup of a lathe, I usually bore a hole about 4" deep and adjust the levelling pads to get a straight bore, on account of it being difficult to straighten a bore by handwork, although a half thousandth is not too awful in that distance.
First you get good, then you get fast. Then grouchiness sets in.
(Note: The opinions expressed in this post are my own and are not necessarily those of CNCzone and its management)