what thickness steel sheet for a motorcycle turntable

A steel sheet that diameter which is reasonably stiff would be pretty thick.

The most efficient solution would be to constructs a frame to support in to steel angle or rectangular tube with a steel or plywood plate on top.

It would probably also be a good idea to put castors and screw jacks around the circumference to give it a bit more stability, reduce the bending loads on the bearings and give you a way to lock it in place. Having support at the edge as well as the middle will also make the whole thing a lot stiffer

You have to think of a positive lock-in mechanism for a bracket or support of some sort, depending on what angle of slant you want to present the bike or do you want to offer a kind of ballast counter weight suspended mechanism so the bike can be easily angled on the display for variety of perspectives.

Even at the most basic configuration you need to have a rough estimate of how the weight will be distributed between the jack and suspension and wheels.

As has been mentioned in other answers it would be better to have a light truss or some base under the plate to make it lighter. But the most important question is the entire tray and the lazy susan have to be strong enough to support both the weight and off-center loading and more importantly it is going to resist toppling ( overturning moment), even during the time of loading the bike on it!

Otherwise the thickness of the plate sounds right at about 1/8" to 3/16". We can approximate the design using steel column bas plate equations.