Try putting down a thick layer of newspaper instead of the black plastic.

Agree no plastic. I don't know exactly what your design is using both rocks and mulch--are there different sections? You'll need to fend off the Bermuda with a strong edge, but even then, improving the soil under the tree with mulch may make the area more hospitable for invading grass. A rock mulch can be a pain if you expect leaves and stuff to drop on it.

This may sound discouraging and it's not meant to--only that it is sometimes hard to "tame" an area under a tree without constant maintenance, or at least weeding. But, that might still look better and be your preference to the bare weedy-grassy look--I'm familiar with that in my yard under trees!

You might start with a smallish area first. Also, even though newspaper allows water through, might check with the tree forum on whether using very thick layers over a large area of the tree root system, plus stuff on top, will allow adequate water. Usually one thinks of adding thin layers of more porous material--but then, some trees are more or less resilient and I don't know anything about yours.

My understanding is you can use grass killer like glyphosate under, around a tree as the product is absorbed by currently growing green plants. Doa search to confirm this but I've done it successfully. It takes several days or even a week to kill and sometimes needs re-application. I try not to use herbicides, however. I have just cut the grass around trees and then mulched with grass clippings and shredded leaves and the grass did not come back after a time. At first some might pop thru and you just put some more mulch over it. You could also try to grow a ground cover to your liking there. I do not like plastic or even landscape fabric, the soil does not do well under either of those.
Laurie

Kill the bermuda with a couple of applications of glyphosate - make sure it's well-watered and growing vigorously before you spray.

Won't kill the trees. THEN, rake out and weed whack or mow the vegetation and spread a sand/gravel mix as a bed for the rocks. You need to have porous surface for the roots of the trees.

Apply herbicide to kill the grass roots. Herbicide shouldn't kill the tree if applied correctly. You might want to consult a pro. Apply it when the grass is happy and healthy. Grass is harder to kill when it is stressed. Then rent a sod cutter to remove the grass. The sod cutter doesn't cut far into the soil, so it doesn't significantly damage tree roots. Apply the mulch/Rocks. Use pre-emerant to keep weeds and grass seed from growing in the area.

I'm with Frankie in wondering whether you've chosen a really good design for the area under a big old tree. It isn't easy to landscape nicely under big trees.

I'm REALLY glad you learned in time where tree roots actually are and to not cover them with plastic. But it's possible you designed your plan when you had your initial impression, that the roots are near the trunk. So maybe a rethink of your design is in order. Any chance you can use the materials you have bought elsewhere in the yard? Or return the plastic?

Trees often create their own preferred ground environment: a mulch of their own leaves. If that isn't working for you, other options would be to add more organic mulch, be it bark or chopped leaves or something else, or growing actual lawn to the trunk, which can work if the grass can get enough light and water (not too often the case). A third might be a perennial garden with lots of spreading plants to cover the ground, such as hostas or ferns. But they will need to be watered to overcome the effect of tree root competition. Any of these options can cope with the shower of leaves from above. Rocks, not so much.

For managing the weeds, is there any reason not to get in there and physically remove the bermuda before you put a mulch down? I'm not experienced with bermuda, nor with whether apricots are very shallow-rooted (and thus vulnerable to digging), but a couple of repeated but shallow attacks on the grass might work. You could always use something like glyphosate if it grows back through the mulch. But I always prefer a hands-on approach to chemicals, if you can muster it.

KarinL

I have a drawf peach tree,I put black garden shhet under this tree,then put marble rocks under it,I left 10 inc. of soil arroung the tree.The tree does well,it is 5 year old and does well with rocks under it.The only problem is once a year,I have to remove all the rocks and clean them,remove weeds and dead leaves.

I'm almost finished readying a new flower bed which is bordered by a partly-Bermuda lawn. I need to dig down at least 4" to be sure I've found all the Bermuda rhizomes (the stiff underground stems which are one way it spreads); apparently that's deeper than normal. If you miss one little bit, it can will regrow. [The threadlike Bermuda roots, unlike the stiff rhizomes, can't start new plants.]

In a quick search, I couldn't find out how shallow apricot roots grow. You could ask your county's Cooperative Extension agent. Or you could wet an area of soil in the middle of the tree's canopy, wait a day or two, then carefully dig a small hole until you find roots that are tree roots rather than Bermuda rhizomes or roots. That would give you an idea of how deep your Bermuda rhizomes grow, and also whether there is an overlap between the Bermuda rhizomes and the apricot roots. If there is little or no overlap between the Bermuda rhizomes and the apricot roots, I assume it would be safe to use a sod-cutter (assuming they even work on Bermuda).

Why remove the grass if it's dead? No sense in disturbing the tree roots. Just mulch over the dead grass and save yourself a lot of work.
Mike

Here is a link that might be useful: My garden