Ideally you'd want a more slender, graceful transition from bow limb to tip. It should all look like it's flowing from one element to the other, instead of limb - cone. If that makes any sense?!
With a drill bit, the entire process of fitting the nocks should be about 5 minutes for both together. My method is (if not using naturally hollowed cow horn):
1. Draw around the drill bit onto the bow tip, and shape it to match exactly. I do this with a sharp knife and it usually takes about a minute per tip. Use a scraper to smooth everything off and make it round.
2. Holding the horn tip in my left hand, I drill down into it holding the drill in my right. This lets me feel if the drill is wandering off centre and I can easily adjust my angle to keep things straight.
3. Push the horn onto the tip, and if it doesn't quite fit sand the tip slightly. If it's a bit further out than sanding will allow, it goes into hot water and then gets tapped on with a light hammer. This water method makes the process take longer but after you've done a few is very rarely needed.
4. Fill the horn with hide glue (or whatever you're using) and shove it on and let set.
5. Mark the position of the string groove and cut down to the wood using a good sharp knife. Open the slot as wide as necessary, round everything off with the knife followed by a wipe of sandpaper and you're done!