You also need to know the straightness tolerance or other form tolerances, since rule #1 from ASME Y14.5 doesn't apply to stock parts. Therefore, your 0.5"+/-.01" bar may be produced at .501" diameter but also bent, thus acting bigger. So what you need is to determine some acceptable worst case boundary that includes size, form, and position (location+orientation), for the stock cylinder once it's already welded in place and then apply the appropriate tolerance to the hole, accordingly.
From ASME Y14.5, 2009:
"2.7.2 Form Control Does Not Apply (Exceptions to Rule #1)
The control of geometric form prescribed by limits of size does not apply to the following:
(a) stock, such as bars, sheets, tubing, structural shapes, and other items produced to established industry or government standards that prescribe limits for straightness, flatness, and other geometric characteristics. Unless geometric tolerances are specified on the
drawing of a part made from these items, standards for these items govern the surfaces that remain in the as furnished condition on the finished part."
If you use a stock part the way you described, you better know how it's controlled geometrically by the manufacturer.