Bermuda grass is a very drought tolerant grass type. Understanding a few key things about it is very importantant. It needs a minimum of 6-8hours of direct sunlight in order to thrive. Temperature is very important as well as humidity. If either one of those are too low, it will cause the plant to be hindered in growth as well. Sunlight directly affects soil temperature which is also important with Bermuda Grass. Soil temperature activates Bermuda Grass as well.
The best length to keep Bermuda at depends a few factors. The lower you keep it, the more you may have to water it as the plant won't be able to retain as much water as it would with longer shoots. .5in to 2.25in is said to be the best length to maintain a healthy Bermuda Lawn. Though some may let them grow much higher, it's really not the best for the grass. You end up with longer clippings left in the lawn over time which can cause thatch build-up over time. It's good to mulch clippings into the lawn during the growing season. Shorter clippings discharged into the lawn will breakdown faster that longer clippings. If the lawn is kept too high, or if it is cut more and a third of it height at one time, it could stress the grass out and cause it to leave discoloration and even kill parts of the lawn off. It will regenerate, but it's very unsightly.
Soil quality is important when trying to keep a nice green Bermuda Lawn. If you are having issues with your lawn thriving, soil quality could be an issue. Proper fertilization scheduling on a monthly basis is another key factor, because you have to feed the lawn and maintain the soil quality as well. If the PH is not correct ( not too acidic or too alkaline ) then the lawn will not absorb the nutrients and make use of them properly. If your soil is compacted you run the risk of water, nutrients, and air, being able to get to the root system. Roots of Bermuda Grass should not be exposed, but compacted soil will ruin growth over time as well. It's recommended that you have an aeration done annually at the time suggested by your turf management company.
If you just purchased a home and you have Bermuda Grass and it doesn't seem like it's growing much or greening up fast enough, it could mean that, the soild could be compacted or the lawn could simply have not had enough time to establish itself. Lawns sometimes take a couple of years to completely establish. If you notice spots that are balding, or have root exposure, you should contact a turf management company that does weed control and fertilization immediately. Have them give you a recommendation based on what they see happening with your Bermuda Lawn.
Trees and Bermuda grass just do not mix. There is a shade tolerant Bermuda Grass available and it does well. It still needs at least 4-6hrs of some kind of sunlight to remain healthy. You may consider removing trees or having them pruned so the correct amount of sushine get to the lawn.
There is a ton of information out there about Bermuda Grass. This is just basic info on what we've seen over time.