We have both young and mature fruit trees and keep a mulch on both. Burmuda grass is a pain. You cannot put enough mulch around trees or shrubs to keep it out. We don't like to use Roundup, but resort to it for this purpose. It is critical to keep it off the shrubs and trees, tho. We handle this by having two people do the job. DH handles the sprayer set to a narrow stream so it doesn't overspray much and I hold a large piece of thin plywood or heavy cardboard next to the wanted plant to protect it. We water deeply once a week except blueberries and they have such shallow roots that we water twice a week. We also rigged up shade for our blueberry plants, using old almost worn out sheets and a support system that allows for plenty of air flow under them. Ft feet off the ground.

It is too hot for me to do yard work so consider what you are able to do. Yes it is good to clear the grass away from shrubs and trees. I use round up if it is a tree with bark to protect it and no leaves close to the ground. I sometimes put round up in a little cup and use a small foam brush to paint just what I want to kill. If you haven't used it before use a little very carefully and gradually get more bold with it. I walk around my yard every day to look for things in trouble. Plants with drooping leaves in the morning need more water. Look at the plants after you water and see how they look when they are happy. Then you may notice when they look droopy.

My suggestion is to keep any grass or weeds 3' from the young tree. Research at OSU and my personal experience confirms that the growth (of pecans at least) can be about doubled by having no competition. This is for situations where there is plenty of water, so the results should be even better when you can't water as well. Mulching adds even more benefits.

At some point, at least for wider trees, the bermuda will eventually not be able to grow under the trees because of shading, and at that time the herbicide area is not as important IMO.