Dick says:

The major reason for using hide glue is that it's removable without damaging the underlying wood. I don't think this applies to a bridge, where removal is apt to be an accident, rather than by intent.

That assumes you locate the bridge exactly right the first time you glue it, with the pinholes (when there are any) lined up and the intonation correct. Otherwise, ya gotta git that sucker off and start over...

P.