He uses a fender mustang bridge, which is the same size as the jazzmaster bridge, but has "better" grooves preventing the strings form slipping off the saddles. A lot of JM/Jaguar players do this (reversible) mod.
J’ first JM he bought from that Slimy Bob character already had a mustang bridge installed I believe. I cannot recall where exactly I read this though.
I’m not sure, but I think some of J’s JMs have some other (not mustang or JM) type of bridge too (tune-o-matic?).