Here is the way I approach mowing Bermuda....
Never, never, never leave the client with brown areas during the growing season. This normally means raising the mower height so that you don't cut the grass down to the stem. The issue with Bermuda is that only the top portion of the blade is green. If it grows to 3", sometimes just cutting it 1" will reveal the brown stems.
The best way to manage Bermuda is mowing at 1-1.5" inches with a reel mower every 3-4 days. Since that is not realistic for many, I did try something new thi s year. On the lawns cut weekly with a reel, I sprayed Primo and Iron during June, July, and August. This has cut the growth rate by 50%, allowing me to cut on a 7-day interval at 1.25" Clippings are mulched and quickly disappear since only a small amout of blade is being cut.
On lawns that are cut with ZTR, I started at 1.5" after Spring scalping. They are now being cut at 2.75" because of the excessive rainfall this year. You simply have to raise the height as Summer progresses. These lawns are not bagged, but often require a second pass to disperse the clippings left behind. Still quicker than bagging.
Also need to point out that these lawns were still being cut at 2" until the hurricanes hit the Southeast. With Bermuda, one heavy week of rain and everything is screwed up.
Even with all of this I stated, you have to manage the fertilizer program very well. Use as little quick release Nitrogen as possible. Try to use slow release forms such as SCU, MESA, or Nitroform.