Who knows what is acceptable on a low-cost lathe? Depends on what you (or they) are willing to accept. Way to check is to chuck up a peice of 1" round about 4 to 6 inches long and take a fine test cut over the length of it. Measure both ends and observe teh amount of taper. I would want it to be less than one thou/.02mm at home. Mr Schlesinger would want a bit less than that on a quality industrial machine.
Is the hole smaller at the headstock end of the job? If so, the taper may be due to spring in the boring bar. Pressure tends to build up on the bar during the cut, pushing it ever so slightly away from the job surface. Best way to avoid this is to take repeated cuts at the end without adding any depth of cut on the cross slide. Do this before you get to the final size, then taking very fine cuts to sneak up on the final size, run the tool through the hole twice at each setting. When you get to size at the mouth of the hole but further inside is smaller, take another pass through, or even a couple.
If the hole is bigger at the headstock end of the job, you may have a small lathe bed to spindle misalignment. One way around this as you say is to bore to say .03 to .06mm or so undersize then ream to finish size.
With your existing tapered bores, you may be able to salvage them by honing, lapping or even reaming to final size to get rid of the taper. A carefully made expanding lap could do the job. I have done similar jobs using a brake cylinder hone, or even a piece of wooden dowel with a saw cut in the end to hold a strip of emery tape spun in the pistol drill and judiciously worked up and down the small end of the bore. I'm sure the purists will arrive shortly with pitchforks and sickles to disabuse you of that notion though.