Simplest way is to use the railroad, the Trinity Rail Express, connecting to DART at Dallas Union Station. The double-decker TRE cars work pretty well for bikes, as do the DART cars if it isn't too crowded. Depending on where you start or finish from, you can still get in quite a few miles riding just going to and from the trains.
Otherwise, I don't have a good route.
The Trinity Trails do extend on around the east side of Fort Worth, although I think those are unpaved gravel trails (should still be fairly smooth). Seems like one of those is supposed to, or maybe already does, go quite a bit east on a different trail. Look on the "Texas Rides" sticky up above, and I have a post with the Dallas bike routes map there. That will get you out of Dallas and out of Fort Worth, the question is what to do between them.
The general problem in this area is that the only roads that go through are major roads, which are sorry ones to ride. So where you need to cross freeway, a lake, or a river, you're very limited on routes.
If I remember right, Hwy 180 where it comes in to I-35 is Bike Friendly Oak Cliff area, and that area seems pretty rideable. Farther west, I don't know about. Up in Irving, Rochelle Road seems pretty rideable, though I haven't actually ridden on it. The section of Trinity Blvd between 157 and 360 has fairly high-speed traffic, though I have ridden on it some. East of 360, it seems much better, and may be better west of 157. People ride around DFW Airport on the service road, Airfield Drive. Otherwise, it'd take some exploring to find a good route.
There was a charity ride going from FW to Dallas (or vice versa),
www.lonestarride.org. I didn't ride it, and don't see a route map, and have no idea where their start and finish points were, or how direct the route was. But might be worth asking them about the route. Keep in mind that they may have had policemen at choice spots, so charity ride routes are not always good general bike routes.
Edit: I just looked at the map posted up there. I would like to point out that North Richland Hills has what appears to be some very good bike routes in town, better than most of the suburbs around here.