You're not allowed to cycle on the A90....
f) I'll take local advice on the A90 toward the Forth Road bridge, because we'll be on it late morning/early afternoon
...
There's a rubbish cycle path somewhere "parallel" to it. If you are planning to come through central Edinburgh, then you should get on the cycle path that follows the disused railway line just past Haymarket, and once you get to the A90 take the back roads - I can check with my boyfriend what the exact route that he used to commute Edinburgh - Rosyth was.
If you are wanting to go round Edinburgh there's a few of us on here who can offer differing suggestions as to routes - I assume you know that you can't cycle on the bypass either, but there is an "inner ring road" that is kind of signposted.
(If you are unlucky enough to hit very high winds it is possible for the Bridge to be closed to cyclists and pedestrians while still open to cars. This can be solved by putting the bikes (and their riders) on the train at Dalmeny (= South Queensferry) and getting off again at North Queensferry or Inverkeithing. Fairly unlikely in summer but worth knowing what you're going to do if it does happen).
I don't think there's any way I can do this, but I'm going to keep an eye on the thread because it sounds a lot of fun!