I have some love/hate groundcovers myself. I think the biggest criteria for my love/hate ratio is the combination of how it grows (fast/slow) and where it is located. i.e. not all fast growers are hated if they are in the right place I just pulled out about 100 sq ft of pachasandra because it just got everywhere. I will miss it in the winter. (pre-snowcover). I have a huge patch of bunchberry (Cornus canadensis) that spreads very quickly, but it is in a part-shade woody tree-shrub area and it really seems to fit the woodland less-manicured feel. I also suspect it would be hard to eradicate if I wanted to. It has those thin roots that go everwhere and break easily. But I love it where it is. I have creeping veronica Waterperry in a perennial bed and it stays put nicely. Love it. I also have Georgia Blue but it is much more aggressive. I have to pull it back severely twice a year. Dislike it (but not enough to remove it). I have a gold variegated one that barely grows. I moved it this year to a new place it may do better. Lamium 'Pink Nancy' wanders and blends in nicely. It pulls out easily if it wanders too far. Love it. Ajuga, love it in bloom (have Choc Chip and Crispa Metallica). Neutral otherwise. Need to have something interesting (and strong) nearby. I'm trying out Hosta Kabitan. Thymes... love the daintiness... hate that they don't suppress weeds so well. Geranium Biokova... I consider that more as a specimen perennial than a groundcover, but I can see it is somewhat of both. Love it. Sedge, Treasure Island...grows slowly, love it because it can go anywhere safely, but unless it is cut back with other perennials, it looks messy far into spring until the new growth covers the old stuff. Cutting back a groundcover is not a fun thing. I used to when I had a little, but now its out of the question. I enjoyed and saved this old thread about groundcovers in link below. I haven't read it in a while, but it might be interesting after reading this thread.

The natural environment of this Bittercress seems to be in flood plains and along rivers and streams indicating it may well need a fairly moist soil to grow in, although it has adapted to grow in dryer soils. I see this growing in lawns that are watered every day but seldom find it in lawns that are watered once a week, which helps point to the flood plain, river, stream areas described by some. You find the same thing with Yellow Nutsedge, it grows in lawns watered daily but seldom in lawns watered once a week. The attached link may provide some help with control. Here is a link that might be useful: About Bittercress

The only popular southern grass that will take any shade at all is St Augustine. Having said that, there is a variety of zoysia called Shadow Turf put out by the Turffalo company just north of Lubbock. Shadow Turf is not popular due to the cost, but it will work in your area. Here is a picture of Shadow Turf growing in the dense shade of an English walnut tree. This lawn was planted 18 months prior to the photo. This picture was taken at high noon, so you can get a feel for how little sunlight actually hits the grass. To the west is a very tall tree across the street which provides afternoon shade on the lot. The tufted area is in a spot to the north of the tree. It started out as 1-inch plugs, so in 18 months those have grown to about 6-inch circles. The rest has knit together very well. The grass is very soft to walk on. This was mowed about 4 inches high (mower's highest setting), but it can be mowed low. Shadow Turf spreads fast once it is established. I tried some in my yard. It sat seemingly dormant from early May to July. Then all of a sudden, it was everywhere up to 10 feet away from where I planted it. So I mentioned St Augustine and then abandoned that line of discussion. St Aug will try to take over your bermuda. This Shadow Turf appears to be fairly compatible with bermuda in that both will invade the other but not dominate. Bermuda will absolutely be the dominant species in the sun and Shadow Turf will dominate in the shade, so there's a balance. Last time I priced ShadowTurf it was $60 for a set of plugs that would cover 100 square feet. But remember I mentioned that it spreads. I might get one tray of plugs and put half under one tree and half under the other. Then water it like it was new turf and wait (and wait). It will not be an instant lawn but it will become a fairly dense lawn by October.

Torpedo grass is almost certainly one of the varieties of bermuda crossbred for extremely high productivity as an animal forage. The closest thing we have in Texas is called coastal bermuda. It is very happy growing very tall or munched down very short. The higher you mow the lawn the less weedy it "should" look. The St Augustine will provide some shade to the bermuda. If you are lucky it will be enough to shade out the plant altogether. Common bermuda is no match at all for any kind of St Augustine when the lawn is mowed at the mower's highest setting. My lawn is a perfect example. It started out as prairie grasses and bermuda. Now it is all St Aug.