My lathe is an Engineers Tool Room BL12-24, very similar to the Warco BH600, or the Chester Craftsman.
It sits on 6 off 1/2 UNF x 20 tpi setscrews. (They started life as bolts but have been threaded all the way down).
With nuts above and below levelling is pretty easy.
My previous Myford 7 was a nightmare to level, as the slightest change of torque on a mounting screw, even when apparently "solid", would send the bubble off on its travels. (There are better ways of spending an evening)
My level is machined from a College Engineering casting, fitted with the most sensitive vial ( 1 div = 0.005" over 12" (0.417mm over 1 Metre) that they offer. It was checked out and adjusted on a surface table in the Calibration Room of the Standards Room at work.
End to end level does not concern me particularly, since it is unlikely to affect parallelism of the work, but twist in the bed does.
With the BL12-24, the most sensitive fixings were the two immediatly behind the chuck, but being able to lock the upper nuts against the lower ones, a 20tpi thread gave a fairly fine adjustment, since one flat produces a movement of 0.0083 inches (0.217mm) in round figures.
Using a level on a Lathe with a vee bedway can be difficult if suitable parallels are not available. In which case, if posible use the level on the top surface of the cross slide.
My method was to adjust at one end only.
With an alignment bar that was within 0.0005 over 12", the tailstock was aligned across the bed.
Needless to say, the gib strips should be adjusted so that slack does not interfere with any of the readings.
It pays to be patient, checking and rechecking, at each end, after each small adjustment, until any twist has been eliminated.
So the only thing likely to result in tapered worki is if the tailstock centre is above or below the headstock centre.
If it is below, it may be possible to shim the tailstock higher. If above, some delicate scraping or machining might bring things back into line (but beware of the tailstock barrel no longer being parallel to the bedways!
Howard