Here is the route I have followed: West on 105 to Navasota. From Navasota take TX 6 to Hempstead. From Hempstead TX 159 to Bellville. From Bellville take the Mill Creek/Cat Springs road to Cat Springs. At Cat Springs join FM 949 all the way down to I-10 and on West to Schulenburg.
An alternative is to stay on 105 to Brenham then take US 290 West to the junction with TX 237 just past Burton then US 77 South at LaGrange.
There are other alternatives, of course, but I have towed our 34' fifth-wheel on both of these.
Texas FM (Farm to Market) roads are generally good, though they may be very curvy.