http://www.robinmathercycles.co.uk/

Forgot the link...

That looks like 5/16". Could be .028, or .035. .028 should be enough for most things that would do. Another thing to consider with the kind of stud mounted into the tube for the bridge, is the fit between something like that headless bolt and the tube. Check the ID chart for tubing and find a close fit. It will probably be a thicker wall than you would want elsewhere on the rack. Also, normally you want metric stuff, but you may need to check out your options, and how a 1/4" bolt would fit your bike, and your ID. Another option is to buy a metric drill bit or better still, a chucking reamer, and ream some tubing to your bolt.