Do you have any other suggestions on how to install bullnose on steps other that nailing or screwing down though the top and then plugging.
This is quite possible if it is the first thing you install, before you lay the flooring material. I assume that this is prefinished floor, and that is why you want no hole in this blullnose.
Cut a small sample piece off the bullnose (just 2″) and use this as a guide to mark some notches in the top part of the skirt stringer. The skirt stringer should come up that high and you want the nosing to fit into these notched slots on both sides. It will look a lot nicer and if you fit the nosing in with great care, it will give tremenduos support. Choose a nosing that has a grooved edge on it. If the skirt stringer doesn’t come that high up the staircase, you may have to undercut the baseboards, and in some cases, only the drywall.
Once the notches are cut, fit the nosing in by cutting it so that it fits under the skirts by at least 1/2″ on either side. You will need to slide it back and forth so that both sides are caught. After you are satisfied with this dry fitting, clean both the nosing and subfloor area and apply a urethane construction adhesive. Some of these urethane adhesives require a misting of water on one piece if the MC in the wood is below 8%. One hint about this fitting is to cut both ends of the flat underside of the nosing with a slight bevel. This bevel needn’t extend to the surface, just bevel the underside ends enough so that they will help you slide it under one notched side and then move it across to the other side.
Once the piece is in place, and make sure during the dry fitting that this placement lines up well with your planned floor installation, you can insert a slip tongue or spline into the exposed groove of the nosing. This will change the groove into a tongue. You should be able to buy pre-made splines from your local hardwood floor shop that caters to professionals. Or you can cut a strip out of 1/4″ plywood.
Glue the spline into the groove of the nosing with a good carpenters glue (let dry a few hours) and then predrill some nails holes and nail down and a 45 degree angle with 3″ spiral finishing nails every 4-6″ on the nosings new tongue. If you are lucky these long finishing nails may hit the framing header, and if not see if you at least contact one of the joists coming off the header. While you are nailing be sure not to kick off the planned line of the nosing. Don’t use pneumatic nails for this, they are all to thin to hold any wood flooring.
Now begin the rest of the installation, fitting the next board (with a small bead of urethane glue under it’s groove side on the subfloor) to that nosing. It’s OK to glue just these two boards to the subfloor (not to each other), although I generally don’t like the practice. Don’t use the nosing for at least overnight, and you will find it is quite firm and quite permanent. You can also glue and nail a cove molding under the nosing for decorative reasons and a bit more support.