This is my tailstock with the live centre and morse extension in place. (You could also make a custom dowel to fit into the quill in much the same way)

The quill is retracted to a set position, in my case it is fully retracted.

There are many difficult ways to measure the thickness of the bottom of a bowl while it is being held by a chuck on the lathe.  This is a very easy way, takes only seconds and is extremely accurate.

Move the whole tailstock assembly forward until the tip of the live centre is exactly at the plane of the outer rim of the chuck's jaws

Setup- do it once and from then on accurate measurement of the bowl bottom thickness will take only seconds

Then scribe a permanent line on the bed where the tailstock assembly is positioned. This line represents where the chuck's jaws will make contact with the outer bottom of the bowl... i.e zero base thickness

How to Measure the Thickness of the Base

With the quill and live centre at its prescribed retracted position, move the tailstock assembly towards the bowl until the tip of the live centre just touches the bowl.

(If worried about scratching a finished surface, use a piece of leather etc.)

Look down at the bed and see how far the tailstock assembly is from the scribed line... and you have the thickness of the bottom of the bowl.

In this case it looks to be about an inch, which is just right for this bowl blank.

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Using this method is so quick and easy you can use it any time

during the bowl making process.

***Just remember to set the live centre to its prescribed position***