The best way I know of to control weeds in Bermudagrass is to use a pre-emergent early in the spring before active growth begins. A safe one would be corn gluten meal. Also keeping the Bermudagrass vigorous with deep irrigation would be helpful. If your trees have an appropriate mulch ring, they shouldn't get too much water from the irrigation as citrus prefer to dry out a bit before being watered. Here's some helpful links.
Corn gluten meal
From this site with lots of helpful info:
"Mulch should be placed around plants to a depth of two to four inches. If trees are planted in lawn areas, an area of mulch should be placed around the tree. The mulch ring should be based on the tree size. A good rule of thumb is two feet in diameter for each inch in trunk diameter. If you plant a two inch diameter tree, the mulch ring would be four feet in diameter. The mulch ring should expand in width as the tree grows until the tree is established. Establishment takes six months per inch of trunk diameter or one growing season for container grown plants. Do not put any mulch within three to four inches of plant stems. Mulch placed against the stem can cause bark decay, root suffocation just like planting too deep, and prevents checking the moisture of the root ball."
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When weeding, the best way to make sure you are removing a weed and not a valuable plant is to pull on it. If it comes out of the ground easily, it is a valuable plant.