When boring, use the largest boring bar you can get up the hole, and make sure the tool is razor sharp and exactly on centre. If it is a thru bore, try to get a small radius on the tool nose, it will give a better surface finish.
If possible, carry out all cutting under power, both in and out, hand feeding will contribute to inaccuracy in the bore surface, and make sure all your gibs are nice and snug, but not tight. You will have enough trouble with tool flex without the machine contributing to the problem.
For your final pass, which should only be a couple of thou at most, go in and out at the same setting at least half a dozen times, maybe a lot more. You might find it is still creating 'fairy hair' for a long time, as it gradually skims off material left behind from the previous cuts where the tool flexed and left you with a tapered bore. Just keep cutting until you get no more fairy hair or dust being produced at all.
For small bores, you can't get much up the bore to measure with any accuracy to see if it is tapered or not. For larger ones, you can use an internal bore mic or a clock bore gauge, but they all come at a price. I have ones going from 1mm upwards, and you don't want to know how much they cost to buy new. But the larger sizes do come at very reasonable prices, around 30 UK pounds for each measuring range.
Don't even think about digiverns for measuring with any accuracy, you are lucky if you can get within a couple of thou, and because of the flats on the edge of the internal nibs, the accuracy is even worse.
Once you have removed the part with the bore from the chuck, never consider putting it back in to remachine if the bore is slightly out. No matter how close you get the settings to perfect, you will never be able to pick up the original bore exactly. Once out of the chuck, the only way to straighten things up is to lap exactly to size.