I wouldn't recommend picture matting for bellows stiffener because
it is layered; that is, it's made of several sheets stuck together.
Only the bottom sheet actually sticks to the leather or cloth and it
can peel off.
A homogeneous stiffener is best. I recommend vulcanized fiberboard,
the stuff often used as valve backing on players. You can buy it in
sheets and it glues down firmly. Hide glue will work fine and will not
cut the bellows material. Use an iron to be sure it adheres fully.
A source for vulcanized fiberboard is Franklin Fiber, 903 E. 13th
Street, Wilmington, DE 19802. They will sell it in small amounts.