I've bleed my brakes over 10 times and replaced the calipers but the brakes are still very mushy and the pedal goes down to the floor. A shop that I just got my car aligned at suggested the master cylinder might need to be bled. What is required to do this? I've read of a "bench bleeding kit" but where would I buy one of those?

 

It doesn't need to be bled, you need to replace the it. Sorry to give you the bad news, but you won't regret it.

 

Most rebuilt master cylinder kits come with a bench
bleed kit. If not, I bought a few for, at the most, $10.

To bench bleed you need to connect the bleeding kit
to the master cylinder. Then securely place the master cylinder
in a benchvise. Fill the master cylinder with brake fluid.
Run all the plastic lines from the bleeding kit into the
resovior. With a piece of wood, push on the master cylinder
rod gently back and forth until there are no bubbles in the
resovior.

Some tips I learned:

If you don't have a benchvise, have some one hold the master
cylinder while you pump it.
Tap the resovior lightly as to surface all air bubbles that may
be trapped in all crevices.