Welcome to TLF fellow bermuda owner! Glad to have you here.
Bermuda does well being scalped when the majority of it is greened up (80%). Best time of the year to scalp bermuda is when it's actively growing, so Springtime. Take it down as low as you are comfortable going, which with your recycler could be 1 1/2" or lower. Go as low as you can, sometimes hitting dirt even. It's going to look bad, but what you're doing is taking off all the leaves that are at the top of the stems, and it's going to look yellow, since there's no leaf tissue down low. Hit it with a pound of N per 1,000 ft², and water it in. You will see an explosion of green within a week's time, and be prepared to mow often when you put that fert on.
Bermuda does well being mowed low, and often. A thick stand of turf is going to be a great defense against weeds. Come Fall, be ready to put down your PreM for the winter weeds. During the summer, you can spot treat the weeds that you have with Celsius and Certainty.
Take your time to read through some of these popular threads Pay particular attention to the
Bermuda Triangle, and the
Bermuda Bible:TNT.