Ruth,
First inflate the ball. Now find a bowl that is slightly lager than the diameter of the portion to be used. Trace the outside of the bowl with a marker. Now cut with a utility knife. The edges don't need to be cosmetically apealing.
Take a piece of foam core large enough to be the backing for the entire piece. Cut a series of foam core circles, each slightly smaller than the previous. This will create your form for the ball portion to be framed. Glue your ball on the form.
Cut a round opening in the mat slightly smaller than the diameter of the ball portion. Now build up on the backing with foam core enough that the mat rests against the ball. Attach your mat to the backing with the ball.
Now complete the piece in the manner you would normally use and your done.
Piece of cake (oh that's a diferent technique).