Ask Mr. Smarty Plants

We are at something of a disadvantage here because you have used a common name for your plant that actually is used on two very different plants, both, however, native to Texas and Bastrop County. These are:

Salvia texana (Texas sage) - Perennial flowering plant, 1 to 1.5 ft, tall, tap root, blooms blue, purple, violet March to May,  native to Travis County and probably therefore to nearby Bastrop County.

Leucophyllum frutescens (Cenizo), also called Texas Sage, and frequently marketed by nurseries as Texas Sage. Shrub, 2 to 8 ft, tall, blooms white, pink, purple, violet January to December. Also native to Travis County.

Neither of these plants propagate themselves by runners. Here is an article from Arizona Master Gardeners Manual on Plant Propagation, illustrating the various ways to propagate different types of plants.  If you follow each of our plants links above to our webpage on those plants you will find a paragraph on propagation of each.

Salvia texana (Texas sage)

Propagation

Propagation Material: Seeds
Maintenance: Trim back the old seed spikes after blooming to maintain a tidy appearance.

Leucophyllum frutescens (Cenizo)

Propagation

Propagation Material: Seeds , Semi-hardwood Cuttings , Softwood Cuttings
Description: Plant seeds in greenhouse immediately after summer collection or store over winter in a cool, dry place and plant outside in spring, after final frost. Cuttings should be semi-hardwood and of the current seasons growth.

If there are any other plants with that common name that propagate by runners, we don't know what they are.