My problem is that whether I use a tenon or a base, the bowl won't
true on the chuck.

If you are working with unseasoned or partially seasoned stock, the problem may
be that the tenon is "moving" and changing shape. What I do is jam chuck the
bowl to be finish turned, true the tenon and outside, then chuck up and work
the inside. Rarely use a dovetail recess, but expect that a similar strategy
might work.

Hope this helps!. If I'm not making myself clear, please feel free to get back
to me in group or by email

Kip Powers
Rogers, AR