To turn a blank on the lathe, it needs to fit in the swing space. It can be helpful to trim the blank with the band saw before turning. I measured our lathe and band saw last night to get the dimensions.
Lathe: The distance from the center of rotation to the bed is 6 inches. That means you can make a bowl that is 12 inches in diameter (probably a little less for safety). When you buy a blank, the distance from the center to the farthest corner must be 6 inches or less.
Band saw: Turning a square blank to a round bowl is tedious. If your blank is thin enough to fit in the band saw, you can trim off the corners. Our band saw will cut pieces up to 3 1/2 inches thick.
Conclusion: Buy/make a blank that is 12 inches or less max width and under 3 1/2 inches thick.
We will be turning tonight if you want to come check it out!