In Houston, the vast majority of lawns are of the St. Augustine variety. There are some Bermuda-based lawns, and Zoysia is gaining in popularity.
Most St. Augustine yards have bits and pieces of Bermuda in them, and it's usually just ignored. Still, some people can find themselves overwhelmed with Bermuda taking over their St. Augustine.
The obvious answer to removing Bermuda is to kill it, till it and replace it with new sod. But that's usually just for extreme cases in which the Bermuda is absolutely solid. In most situations — a mix of Bermuda and St. Augustine — simply mowing properly will help the St. Augustine win the battle. If you mow as tall as your mower will allow, the St. Augustine will almost always crowd out the Bermuda. (Conversely, if you want to accelerate the Bermuda, mow shorter and more often. Then the slower-growing Bermuda will win, unencumbered by shade from the taller St. Augustine.)
If you allow your grass to grow taller, you'll still have to mow once a week. But if your neighbors don't come up to your level, it will look like you don't mow at all. I promise, though, your lawn will be a richer green with a thicker texture than your shorter-cutting neighbors. And there is an added benefit to growing taller-than-normal St. Augustine — you won't need to irrigate as frequently because tall grass supports deeper roots, which will reach water that's far down in the soil.
Another benefit that comes with taller grass is more biotechnical. Grass blades have microscopic pores (stomata) to transpire carbon dioxide (CO2), oxygen and water vapor. The stomata open in the morning and close when they get their fill of CO2. Since taller grass has more stomata exposed, it more readily collects CO2 released by soil microbes. And, since CO2 is heavier than air and tends to remain close to the ground, it's harder for wind to blow it away in taller grass. Therefore, tall grass gets more CO2. And, as a consequence, the stomata close off earlier in the day shutting off the transpiration of water vapor and allowing the plant (and soil) to better retain water.
Yes, I know that was way more technical than you probably needed, but I really like researching this kind of stuff for you.
Also, Bermuda does not suffer from drought damage, as a St. Augustine yard might if ignored, say, during a summer vacation. Nor will it suffer chinch bug damage.
Of course, beyond mowing tall, you should absolutely be following my fertilization schedule — well-cared-for St. Augustine mowed tall will take over!
I have also been known to recommend the use of liquid atrazine to battle Bermuda grass. While I abhor the use of atrazine-based weed-and-feeds, spot treating with the liquid can make Bermuda very sickly and further hasten its demise.
Finally, for those who have a yard service that mows every customer's yard the same, you're the boss — you pay the tab, so make sure to get out in front of the crew the next few times they show up and remind them that you want your grass mowed taller. If they refuse, well, you get to fire them. There are plenty of lawn-mowing services that will do as you request. I have found, through experience, that once you've instructed them cut your lawn taller a few times, they will remember to do it in the future.
IMAGES: Florida Environmental, Lawnstarter