For most work the best solution is to reverse chuck it and turn the base.
For bowl turn a jam chuck from a block of waste wood. this is a bowl shape piece about a 1/3 to 1/4 the diameter of the bowl.
Put the bowl over the jam chuck with a pad (dense foam, leather, paper towel, etc) between the two wood surfaces and bring the tail stock up to hold the bowl in place. You will need to center the work so keep making slight ajustments in the tailsock position until it is running true.
turn away the face plate block or chuck mount.
The same process is used to true up a roughed out bowl for mounnting on a facelpate or chuck. the roughed out bowl can be reverse chuck directly on the jaws of the chuck since you will turn away any marks. Touching a pencil lightly to the faceplate block will leave a mark on the most off center part.
This reverse chucking method is simple, does not damage the rim and works well with etremely thin pieces too.
The same process is used for hollow forms but the jam chuck pieces need to be different
Happy Turning,
Al