I think most responses will advise 1/8" to 1/4" of sapwood, with maybe most leaning toward 1/4".
This, of course, is barring any additional information that might preclude the ~1/4" or so advice (e.g., stave back irregularities; presence of troublesome knots; low density; heartwood issues, etc.).
I just finished my first yew self bow. I ended up leaving about 3/16" of sapwood, on average. I also backed the bow with some nice rawhide, the whiter kind that matched the yew sapwood better than some of the more tan & semi-translucent stuff. The bow stave had a few troublesome knots on the very edge of one limb, and a few punky holes I plugged. So far the bow is holding up great. And it's quick, too. 62" nock-to-nock; ~56# @ 26.5" or so.