I may have not been correct in making a statement that makes it sound like bermudagrass is a broadleaf plant.
On the other hand, glyphosate is effective at killing bermudagrass.
From the Roundup Original label
Product Description: This product is a postemergent, systemic herbicide with no soil residual activity. It is generally non-selective and gives broad-spectrum control of many annual weeds, perennial weeds, woody brush and trees. It is formulated as a water-soluble liquid. It may be applied through most standard industrial or field-type sprayers after dilution and thorough mixing with water or other carriers according to label instructions.
When reading the label, bermudagrass is mentioned a number of times as plant that can be suppressed with Roundup. However, the OP should read the label to make sure Roundup can be used in her environment and is suitable for planned use.
Also from the label in bold lettering
AVOID CONTACT OF HERBICIDE WITH FOLIAGE, GREEN STEMS, EXPOSED NON-WOODY ROOTS OR FRUIT OF CROPS (EXCEPT AS SPECIFIED FOR INDIVIDUAL ROUNDUP READY® CROPS), DESIRABLE PLANTS AND TREES, BECAUSE SEVERE INJURY OR DESTRUCTION MAY RESULT.
Not all products recommended on this label are registered for use in California. Check the registration status of each product in California before using.
Read the entire label before using this product. Use only according to label instructions.
It is a violation of Federal law to use this product in any manner inconsistent with its labeling
FWIW, the document I linked to is 21 pages long.