I've heard to mow a lil' higher than normal, the st. augustine will shade out the sun thriving bermuda. Before the winter I had a 8'x8' area of pure bermuda. Afraid it's just going to keep spreading. Hate it. Have tried pulling it out, that's just pissin' in the wind.
You have 2 choices. Option 1 is to mow your St Augustine taller (it should be cut 3.5 - 4 inches), fertilize and water it correctly, treat it for any diseases and get it healthy and it will eventually choke out the Bermuda. Option 2 is to spray it all down with RoundUp, give it a week or two to kill it all out completely, scrape all that dead grass off, till in some good topsoil, level it out and resod. Option 2 is faster but Option 1 is easier.
Healthy St. Augustine will choke out Bermuda but it won't happen overnight.
When the summer heat comes. Yes a healthy Saint Augustine Grass will in fact choke out the Bermuda grass.
Use Scott's Bonus S. This will get rid of the weed's and let more air get into the soil.Then after the weed's are all gone.Rake the Yard from corner to corner. Saint Augustine need's to be free of all weed's and debris. For this promotes healthy steady runner growth.Which in turn will fill in the rest of the Yard. I hope you have a thick Green Lawn.
I figured there was no "miracle" herbicide that'll kill the bermuda, and not the st. augustine. What's weird is the back yard has a moderate amount of weeds & bermuda, but the front has zilch! Struggled with dallis grass in backyard last year by spending countless hours pulling by hand. Only saw 2 clumps of it this past wkd. Just put down Scott's Weed & Feed. Hopefully that'll keep the crabgrass out.