Make certain that the router bit rotation cuts into the grain and not prying the fibers apart. Make shallow cuts several passes. If bearing guided bit, change to larger bearing and then to smaller bearings for subsequent passes until you reach the desired diameter. Sanding is safer. I tend to prefer round over bits over bull nose bits. The end result is the same, but the bull nose requires exact board thickness to get proper results. Doing one edge at a time with a round over bit doesn't require the board thickness, but does require using a router table and fence, at least on the second pass, and a zero clearance insert closely fitted around the bit profile, because the bearing will not have wood to follow during the second pass. If you try it, you will get a deeper cut and a step in the edge because of this. The bearing will want to ride on material that was cut away during the first pass.
Charley