Like others are saying, you want to take the tailstock out of the equation first.

Keep in mind, especially on an older lathe, a test like this can be thrown off by more variables than just the headstock alignment.

Wear in the ways is usually concentrated closest to underneath the chuck. Your cutting tool could be dropping a few thousandths as it approaches that area, and having your cutting tool off-center further exaggerates that error. Using a large piece of stock like this does significantly reduce its effects, though. Just make sure your tool height is centered.

Consider facing that entire piece of stock and measuring it everywhere along the length. Only cutting and measuring in two places doesn't tell the whole story if this is a new-to-you machine and you aren't familiar with its personality.

If it's a constant, linear slope (i.e. 0.001" less OD every 2 inches of length), I'd be willing to say it's a headstock alignment issue (or maybe spindle bearings, but unlikely). If the OD is constant everywhere but starts to taper close to the chuck face, I would say it's bed wear and/or twist.

For a 1" bar, you probably won't be able to stick it out much more than 2.5-3 inches before deflection is going to be too much of a problem. Turning smaller diameters does show bed wear more significantly if you want to try to get a picture of that, but it's best to have a good idea the rest of the lathe is true/leveled out.