Currently openjdk uses java-access-bridge which relied on bonobo in the effort to remove bonobo a new project java-atk-wrapper has been created http://git.gnome.org/browse/java-atk-wrapper/ . It would be good if openjdk doesn't bring obsolete technologies like bonobo with itself.
It looks like java-atk-wrapper is completely broken: https://bugs.launchpad.net/ubuntu/+source/openjdk-6/+bug/935296
Review request for java-atk-wrapper is bug 820361 Once that's in, I will add the bits to openjdk to set it up as the default accessibility provider. It works with basic swing programs as far as I can tell; I haven't done extensive testing.
Pavel has graciously accepted the task of testing out java-atk-wrapper to see if it's a good (enough) replacement for gnome-java-bridge to be used by default.
Move to rawhide for consideration.
Fixed in F19: http://koji.fedoraproject.org/koji/buildinfo?buildID=408796