Much depends on the size of the bowl and the type of edge that it has.
For natural edged bowls, which couldn't beheld in cole jaws (or anything similar) I have a big lump of wood mounted in my chuck, which I then skim the face off so that the inside of the bowl sits nicely on it, then I face it with a soft cloth, slip the bowl on and bring the tail-stock up to it. If I don't want the centre on the tailstock to mark the wood, I have a range of firm, rubber/plastic objects ( like tap washers and door-stops) that I use to press the bowl in place. Simple friction then provides the drive.
For clean-edged bowls I use cole jaws up to their maximum diameter, but above that I have two other types of reversers. One is very simple. It's a huge disc of plywood with excentric circles marked on it at 1cm intervals. have a few different sets of 'buttons' made from scraps of wood, that I bolt onto the plywood at relevant diameters, to sit the bowl or platter into. This comfortably holds platters and large bowls up to about 28" diameter.
I also have a special, home made chuck that is based on two disks of plywood bolted together at the centre point. There's a series of curved grooves routed into them, one set swinging clockwise, the other anti clockwise. Buttons for holding bowls or platters are then bolted on, through the intersections of the two slots. You can see it, and other ideas, in this thread of Bryan's.
http://www.awgb.co.uk/awgbforum/index.php/topic,2243.0.htmlLes