When a falconer wants to keep his bird quiet, he'll put a leather hood over his head. A bird of prey won't hunt what it can't see. Another restraint is leather straps on the bird's feet. This is what Isabeau contemptuously dropped in front of the bishop.
I think she cut her hair because in her wanderings with Navarre while they were still under the curse, Isabeau may have found it expedient to occasionally disguise herself as a man. It would have been easier with short hair.

What she held out to the Bishop was a leather strap that falconers use to restrain their birds. The symbolic meaning was 'I am free, now.'
As for cutting her hair, it was short throughout the movie; it was 'feathered,' which was a very popular style, at the time, symbolizing her connection to the hawk that she transformed into.
As always, I could be wrong. As usual, I probably am.

• Crazy. All crazy but I'm.