Fist, I use and recommend the Niles stopper mandrel. I have the PSI screw on mandrel as well as one for the mini stoppers which needs to be mounted in a drill chuck or collet chuck. All work well and do what they are designed to do.
You can of course make your own from a bolt as mentioned and attach to the lathe with a drill chuck or collet chuck.
The one thing which I haven't seen mentioned yet is that your bolt mandrel should include a shoulder for the bottle stopper to screw up against when tightened....the same as any of the purchased BS mandrels and also the same as your jaw chuck which screws onto the spindle. They all need to register up against the shoulder on the spindle to run true. A chuck will wobble if not seated fully against the shoulder on the spindle.
A bottle stopper blank needs that support as well. It gives stability to your blank while turning and can be your sizing guide as well.
It will be square with the stopper when assembled.
Just take a scrap of hardwood, acrylic, Corian, or anything hard, drill to slide onto the bolt. Figure your length to have the correct amount of bolt threads exposed and epoxy this sleeve in place. Then with the bolt mounted, turn the sleeve to desired diameter and square the face(end in which the bottle stopper blank will contact when screwed on).
This should give you the best results when you turn your stoppers.
Good Luck!
