Will,
Here are some pics of 603s with different wheels.
Bristol Cars - Owners and Enthusiasts Forum - penman's Album: 2008 Concours - Picture
Bristol Cars - Owners and Enthusiasts Forum - Kevin H's Album: BOC Concours 2000 (UK) - Picture
The second one shows a 603 wearing early XJS wheels.
I guess it doesn't matter if the Jag uses bolts and the Bristol uses studs so long as the Bristol wheel nuts mate well with the surface of the Jag wheels so they can be torqued up sufficiently and cannot move. Of course we don't know which wheels the grey 603 had beforehand - the nuts for the Bristol steels are different to the nuts for the Avon wheels.
Kevin