Put this under the worst advise ever.

DO NOT "bash out" the headset cups! It's a bicycle, there are very few thing you would ever bash out.

The quickest and easiest way to remove the cups is using the Park 'rocket', use it with a tap, tap, tap and the cups fall out with out damaging the headtube(the part they fit in).

You can make one that works by cutting slots in some 3/4 copper pipe and spreading the ends so it look like the park tool. Put a cap on the other end, and tap, tap, tap.

OR, you can use a brass drift to tap out the cups. Tap them going side to side from the inside, working your way around the cup. Just tap, tap, tap. No need to use excess force, or bash them out.

Or you can use a piece of pvc pipe as a drift, this is gentle on the cups(if you care). Again tap, tap, tap around the cup and they will come out.

The reason you don't want to bash them out, but get them out evenly is that if the come out crooked you can distort the head tube. This will make getting new one in that much more difficult.

For future reference, a few taps with a deadblow hammer on the top of the steerer tube, then under the fork crown will loosen up the tapered ring of the head set.

And don't use a screwdriver, that's the wrong tool.