I use hot hide glue to adhere bellows cloth.  On MDF, so much of the
gluing surface is made up largely of resin that I doubt hide glue could
penetrate into the MDF board much or adhere to it otherwise.  This may
not make for a great bond.

Screws in MDF strip easily.  I believe the Universal Piano player
system uses carriage bolts which go completely through the MDF.

Bill Maguire