Morgan,
I think you do not have a ring washer under the plain bridge washer in your upper picture. That is why the bridge washer can turn.
First picture here shows what you should have, either the plain bridge washer with a separate ring washer ( on the left) OR a bridge washer with swedged on ring washer (on the right).
Second picture shows a selection of plain bridge washers, wing washers (made to be separate pieces from the bridge washer), and bridge washers with swedged on ring washers that were intended to stay together as an assembly.
Plain bridge washers are intended for use by themselves, without any ring washer ( either as a separate washer or swedged to the bridge washer), on stems that are vulcanized to the tube with a rubber vulcanizing pad as in the upper picture in my first posting ( which is a modern drawing of reproduction stem and tube).