I would suggest buying a fully rebuilt \ re-man master cylinder and bench bleeding it. Typically you can rebuild your master at home with a kit with new seals etc etc, but for the hassle , I much prefer a rebuilt \ re-man master cylinder for a few bucks more.

Bench bleeding will remove most of the bubbles \ airt but it seems like inevitably you have to pop off each wheel and do a full brake bleed, which is a pain, but necessary to regain that firm pedal and get rid of the mushy feel.

Yasin