How to remove a 'press fit' steel ball bearing?

I'm doing some work to my Russco turntable. I need to replace the ball bearing in platter shaft. This bearing is pressed into the end of the platter shaft and cannot be just 'popped' out. It has to be forced / pulled out. Being pressed into the shaft, there is no way to get a grip on it to pull it out. Someone suggested that I heat the end of the shaft which would cause it to expand so the hole in the shaft would get bigger and the ball bearing would drop out. I tried that to no avail. Someone else tried to explain a removal method but I think he never really understood how this bearing is set. So, I'm going to try to explain this so that it is more clear.

Imagine that you are holding in your hand a 6" long steel rod of about 1" diameter. You turn that rod so that you are looking directly at one of the ends (you are seeing a 1" diameter circle). In the center of this end a hole of about 3/8" has been drilled. Into this 3/8" hole a ball bearing has been pressed so that approximately 1/2 of that steel ball bearing protrudes from the end of the shaft. How do you remove it?