I have usually estimated bowl bottom thickness using a rod touching the bottom and sighting across the rims, then holding the mark move it to the outside and sight. I found I often missed the true thickness by 3/4 inch. If I took the bowl off the dovetail chuck and did a caliper measurement from the base of the dovetail recess to the inside bottom of the bowl, it often would not run true on rechucking.
On ABPW is a rough drawing of how I made a dedicated caliper. It measures from the shoulder of the dovetail jaws but indicates the true thickness of the bowl bottom to the dovetail recess, while leaving the bowl on the chuck.
I should modify the instructions to cut off the nib and tip of the straight leg first and check the measurement on the empty chuck. It may be possible to trim both the bowl side and the back side of the straight leg of the caliper to adjust for zero. I wound up taking too much off the curved tip and had to epoxy a dowel tip on, but it works great for me. It is easy to measure and tell how much more wood to take out without making a flower pot with a hole in the bottom.