+/- .0003 is a six tenth window. Easily in the three point micrometer range. I have SEVERAL different ways to measure bore sizes- Comtor gages for every size bearing bore in my line, Brown and Sharpe intrimiks to 7 inches, Standard Brand bore gages, Deltronic Pin sets in tenths, and Diatest bore gages. Since you're only trying to make parts to 1 1/2 inches, at least measuring to high accuracy- you're lucky.
The Diatest sets are really nice, with included rings in fairly small increments. I TEND to use these more than the others. If you only have a few sizes of holes, the Deltronics TENTHS sets are also very nice. Pins in tenth increments. I have these pins in the common sizes I grind parts to. With a bore gage and pin set, I know I'm within a tenth.
The Brown and Sharpe intrimics are available down to .350. These also are quite capable of measuring to your tolerances. For my large bearings, I use these along with a ring gage for all my bearings. The Intrimics are a THREE POINT micrometer, which is a little easier to get centered. I HAVE COMTORS for every size too, but for some reason, have more of a comfort zone with the Intrimics. The real key for accuracy is a certified ring gage so you KNOW what the correct dimension should read.
Comtor bore gages have been around a LONG time, and since they have, there's been a TON of them on ebay. I bought out a machine tool company, and got ALL of their bearing sized Comtors. What a score! Comtors are SUPPOSED to be idiot proof, but I still think they need a feel to get them square. I have brand new Comtors, that I couldn't get to repeat each time- not off by much, but still they wouldn't repeat. The Standard brand bore gages for my large sizes with .0001 indicators, I like a lot. When I do bearing bores, I tend to check and recheck using MORE than one instrument.