you've GOT to be joking.  It's going to be a century at the minimum.  By the time you avoid major highways, it's going to be a full 200k.

DART on the Blue line to Ledbetter station will get you around most of the Metromess, then I suggest using BikeRoute Toaster and Google Maps to plan a route from there. Use the Google autorouter on the Toaster, that other autorouter is worthless unless you like taking long detours out of your way to use major highways after you tick the "Avoid Highways" box.
 
Edit: I'm such a nice guy I saved you the effort and did it myself. This route will dump you at the NE side of Glen Rose on US 67.
 
Leg (mi)      Total (mi)      Name      Directions
0.0      0.0      Straight      Head southeast on S Lancaster Rd/TX-342 toward Shellhorse Rd Continue to follow TX-342
15.0      15.1      Turn Left      Turn left at N Hwy-77/US-77
5.0      20.1      Turn Right      Turn right at W Hwy-287 Byp
4.2      24.3      Turn Left      Turn left at Sardis St
0.0      24.3      Turn Right      Take the 1st right onto US-287
9.2      33.6      Turn Right      Turn right at Ward Rd
0.6      34.2      Straight      Continue on E Wyatt Rd
0.7      34.9      Turn Left      Turn left at S Wyatt Rd
0.4      35.3      Turn Right      Take the 1st right onto S Hwy-67/US-67 Continue to follow US-67
 
Created bywww.BikeRouteToaster.com
 
Total distance 82.15 miles with 1397 feet of climbing
 
The route looks fairly good with wide shoulders most of the way, remember to use caution at the I35E interchange with 67, and the autorouter took you around the tricky parts at the 287/67 interchange.