The one in my video is made from a high pressure gas cylinder (6000 or 10000 psi, can't remember which) and it has about 3/4" walls. I consider it more than satisfactorily strong for the purpose. We do, however, evacuate the immediate area when firing it.
Since bowling balls are not a standard size (from the perspective of tubing diameters), you will need a large lathe to increase the bore to about 8 5/8" so the balls will fit.
Assuming (a big assumption) that you could limit the mortar to being fired with a powder charge appropriate for a range of 200 yards (not much powder, by the way), I would be satisfied using 8" ID, 1" wall seamless tubing bored out to fit. You would have a wall thickness of 11/16" which should be adequate. The problem is dealing with someone who wants longer range, either while you have it or after you have gotten rid of it.