Ask Mr. Smarty Plants

The short answer is that your best bet is to get out there and dig up the offending plant.

This is kind of an awkward question for Mr. Smarty Plants since the mission of the Lady Bird Johnson Wildflower Center is to promote the use of native plants and it appears that you have a situation where one non-native species is invading another non-native species.

You don't specifically identify the bluestem you are having a problem with, but Mr. Smarty Plants suspects you are talking about King Ranch bluestem (Bothriochloa ischaemum var. songarica), frequently referred to as KR bluestem or KRB.

KR bluestem was introduced from Europe and Asia, and has greatly increased its range by cultivation for livestock forage and as an inclusion in seed mixes used to stabilize roadsides by highway departments. When it was introduced in the 1920s and 1930s it was seen as a desirable species for erosion control since it is drought resistant and quickly establishes itself. This plant is now considered an invasive species and its presence threatens the abundance and diversity of native species.

St. Augustine is also non-native that has been imported from tropical regions.

Here is another Mr. Smarty Plants answer to a similar question with a link to an even earlier answer that goes into some detail about eliminating KR. You'll see that the methods discussed are probably not practical in a home yard, so back to the digging.