Roundup should be fine on bermuda right now, it should be dormant just check for green up. If Bermuda grass is breaking dormancy and greening up don't spray it with roundup. Don't use roundup period on St. Augustine or Zosia they never really go dormant. I have watched folks sod their yards with Zosia or St Augustine spend a fortune then spray it with roundup and kill it.
I would be cautious about spraying atrazine, metolachor or pendimethalin with a pump up hand sprayer. It is going to be hard to get proper rates applied. Might want to try and find a neighbor with a pull type lawn sprayer for that. If you get rates to high you can end up with bald spots in lawn where grass will not grow for some time. I have a backpack sprayer with a 6' research boom that works for small areas easy to calibrate by speed that you walk.
Several have already mentioned weed and feed. That is a pretty easy and safe way to get residual herbicides out. Just read label adjust the push spreader or pull behind spreader to settings on label. It is fertilizer impregnated with atrazine or simizine and usually metolachor. Rainfall activates the herbicides once the stickers pick up atrazine they die. The biggest drawback here is expense. It is reasonable for a small lawn and is easy to apply but to expensive for me with 7 acres to treat plus I don't want to fertilize that big of area. It wil add to my mowing trips and take away fishing time! Lo!
Good Luck!