Rick,

You did not mention if graphite or bamboo, but, I have removed the broken tip material from the metal tip by the following methods:

I have never broken the tip off a bamboo so not sure if what I have done will work on it or not, but, for graphite if there is any of the graphite tip material exposed, I have gripped it with a pair of needle nose pliers and heated the metal tip top with a lighter and just pulled the graphite out of the tip. It does not take much heat to do this. If no material is exposed, I have taken a very small drill bit and held it with a pair of pliers and just screwed the tip top onto the drill bit and then heated the tip with a lighter and grasp the drill bit and pulled the material out. The above may work on bamboo, but, since a bamboo tip is not hollow, you may be able to use a very small drill bit and screw the tip top by hand onto the drill bit to make a small hole. Then take a very small screw and screw it into the hole you have made and heat the tip top with a lighter and grasp the screw with pliers and pull the bamboo material out.

Just thoughts and ideas that have worked for me....