The Safe Passing Bill (SB 488, HB 827) has been introduced, referred to the Senate Transportation & Homeland Security Committee and the House Transportation Committee, and recently heard by the House Transportation Committee in the public hearing this past Tuesday.
So you're probably asking now what? Well now we wait. We wait for the House Committee to vote for it (or amend) and we wait for the Senate Committee to host its own public hearing and vote on it (or amend). Then on to the Floor!
The Texas Legislative Council maintains a website dedicated to explaining the Texas legislative process with a cool diagram. Although not nearly as entertaining as childhood favorite, How A Bill Becomes a Law by Schoolhouse Rock, the website is incredibly informative!