Sec. 545.057. PASSING TO THE RIGHT.
(a) An operator may pass to the right of another vehicle only if conditions permit safely passing to the right and:
(1) the vehicle being passed is making or about to make a left turn; and
(2) the operator is:
(A) on a highway having unobstructed pavement not occupied by parked vehicles and sufficient width for two or more lines of moving vehicles in each direction; or
(B) on a one-way street or on a roadway having traffic restricted to one direction of movement and the roadway is free from obstructions and wide enough for two or more lines of moving vehicles.
(b) An operator may not pass to the right by leaving the main traveled portion of a roadway except as provided by Section 545.058
Sec. 545.058. DRIVING ON IMPROVED SHOULDER.
(a) An operator may drive on an improved shoulder to the right of the main traveled portion of a roadway if that operation is necessary and may be done safely, but only:
(1) to stop, stand, or park;
(2) to accelerate before entering the main traveled lane of traffic;
(3) to decelerate before making a right turn;
(4) to pass another vehicle that is slowing or stopped on the main traveled portion of the highway, disabled, or preparing to make a left turn;
(5) to allow another vehicle traveling faster to pass;
(6) as permitted or required by an official traffic-control device; or
(7) to avoid a collision.
(b) Omitted by author for brevity and because it does not apply to our discussion. Look it up if you don't believe me!
(c) A limitation in this section on driving on an improved shoulder does not apply to:
(1) an authorized emergency vehicle responding to a call;
(2) a police patrol; or
(3) a bicycle.
Well, there you have it. There is a very narrow set of conditions that allow passing on the right in Texas. Outside of meeting those conditions, it is illegal to to pass any vehicle operator to the right! Essentially, the only time you can pass on the right is when the vehicle you are overtaking is preparing to turn left.
Furthermore, it is against the law to to use the shoulder to pass a slower vehicle, except under the same conditions as those that allow passing on the right.
On the vast majority of my travels, I am on multi-lane roads or two lane roads without an improved shoulder. As none of these roads have lane widths over 14 feet wide, I ride my bicycle in the left tire track of the right-most through lane. Overtaking vehicles pass me with little or no delay.
But sometimes I ride on two lane roadways (One lane for each direction of travel) that have improved shoulders. About one out of five Texans elect to pass me on the right shoulder, sometimes when they have no impedance to passing me legally on the left. What's with that?
In fact, I have had two motorists pass me on the right when there was no shoulder at all, with two of their wheels about four feet into the verge. (Another woman attempted to pass me on the right but failed when she nearly hit a mailbox before falling back in behind me.) There is no provision in the law for this maneuver. Sec. 545.057 says "On a highway having... sufficient width for two or more lines of moving vehicles in each direction" or on an "improved shoulder". (Sec. 541.302(6) "Improved shoulder" means a paved shoulder.)
It would seem that there are numerically more scofflaw motorists than there are scofflaw bicyclists. There seems to be a lot of driver's license holders that could use a refresher on the laws governing overtaking slower vehicles. For your convenience I have posted those sections of the law above.