Here in FL, when Bermuda gets in lawns it tends to take them over with time. I would over seed the dormant areas with more rye seed so its not an eye sore this winter.
I wouldn't spray the lawn with round up unless your planning on sodding the whole lawn. Killing everything will only invite more weeds to take over before any grass seed will take in the growing season.
Regular mowing etc... I believe it will take care of itself. If your patient, that is also the most economical approach. Good luck!