Whether it is the longworth chuck or cole jaws they are OK but I would tend to use the tailstock to hole the piece while any work is being carried out, you may get away with light cuts but great care should be taken all of the time. For a better hold then a doughnut chuck would be the better option but you will need to make them. The advantage of doughnut chuchs is that you can clean the bottom of nateral edged bowls with the addition of a jam chuck under the bowl.
All I use to clean the bottom of bowls is a jam chuck with the tailstock brought up with a ring centre. clean off as much as possible then take the little stub off by hand and sand