On the second link I've got some maps on post #10 that will get you to Ashland.
I don't know the bikeable routes from Ashland through Richmond. Route 1 / 301 seems to go straight through, but there may be better or nicer ones.
If you have any questions, just post them.
Since you're starting at Dulles, here's a map to get you to Old Centreville Road / Manassas. I think you can bike through the north service entrance. Through Herndon to the W&OD Trail, then the Fairfax County Parkway (side path all the way) to Stringfellow. http://www.gmap-pedometer.com/?r=5122100
November, Trek OCLV, Bianchi Castro Valley commuter
Can't help towards Richmond, but I'd describe one part of cc's excellent route suggestions out of Dulles as "scary" - VA 606 can have fast, heavy traffic (esp. rush) from Rt 28 to the Herndon line, and the shoulder, such as it is, is gravel. Although the immigrant laborer demographic seems to navigate it successfully if slowly on weathered MTBs. Plan B: taxi or hotel shuttle to Herndon, ride from there. The Washington Dulles Marriot (several decent restaurants next door in the "Worldgate" complex) is at intersection of RT 267 (Dulles Toll Rd) & Centreville Rd. The former Days Inn, now "Crowne Plaza Hotel Dulles Airport" is across the street. Centerville Rd is bikeable (I use it daily) and has a usable side path to US 50. You can access the Air & Space Musesum Annex by bike (Wall Rd, A&S Pkwy across 28), but that road is blocked south of the museum towards 50.
cc's routes look better from S of US 50 to Manassas vs Centreville Rd. (Stringfellow is definitely a milder road than Centreville Rd - less and slower traffic.) I think Centreville rd - Walney rd - Westfields - Poplar Tree - Braddock - Stone - to 29/Lee Hwy would work; crossing 66 on Lee may be tricky, then onto the balance of his route. Rt 28 is NOT bikeable (safely or legally) until a side path that starts somewhere south of the Rt 29 intersection. I think his route in his 2nd link uses that or something close.
This is a great time of year for riding around here (assuming we're done with excessive rainfall and the odd earthquake for a while). have a safe flight & trip.
The US Bike Rt 1 is further east - I think you'd have to connect to the W&OD Bike Trail (a bit N &E of Dulles iN Sterling or Herndon) and take it, Custis trail, and Mt Vernon trail to reach it. Or the FFx Pkwy side path (which vanishes between US 50 and I-66!) to Rt 123, then 123 to Occaquan VA I think gets to it eventually as well.
I've never ridden 606 (I drove is twice a week through most of the spring and summer) and I agree it's not ideal, but I often saw bikes on it they seemed to be doing ok. A short stretch on the W&OD, and the FC Parkway sidepath to Stingfellow avoids all the nonsense along route 50.
Bus or taxi out of the airport is a good idea.
Strongly recommend NOT taking US Bike 1. It will add a lot of miles to your trip to get to it, but it also sends you down (imo) some foolishly dangerous roads in southern Fairfax and northern Prince William. Going through Manassas instead of Woodbridge avoids the mess.
ps I'm convinced the main reason BR1 goes that way is to show off the Mount Vernon Trail. It is a beautiful ride, but since 2001, not being able to pass through Fort Belvoir to safer roads makes it a DEAD end.