As of last year when I looked, US Highway 79 had a 130 mile stretch with very wide bikeable marked and paved shoulder all the way from the east side of Thorndale, TX to Palestine, TX. US Hwy 79 has no shoulders to speak of between County Road 123 to Thorndale, but there is a network of county roads that could take you from Old Settlers Park in Round Rock to Thorndale.
There's a tremendous amount of construction around Round Rock so local information gets outdated real fast.