Your lathe might have come with a live center. This is a cone that will
freely rotate. You'll also need a dead center ,which is a cone that will
NOT rotate. The dead center is your drive center. Your usual bushings
might work, but it is better to get a set made for this, as they are
usually chamfered to match the angle of the live and dead center
so you don't get movement. Some members in this forum make them
and offer them for sale.
You'll need the centers to have the same morse taper as your
lathe. Most mini lathes use a #2 taper, some use a #1. Larger lathes
might use a #3 morse taper.
There are some members here who sell them and most tool suppliers
will have them. I usually try to buy here first.