Round Up is glyphosate. Their patent on glyphosate expired some years ago so now there are quite a few other brands that are much cheaper. What you're looking for is 41% glyphosate. Tractor Supply and Walmart both carry house brands that are at least half the price of Round Up. The way it works is the glyphosate is absorbed by the leaves and from there is pulled into the roots where it kills the entire plant. If your orginal application beaded up and rolled off then that explains why it didn't work. The soap combined with a fine mist should fix that problem. As far as the bees go, I don't think it will bother them as they most likely won't get in it anyway but I'm not a bee expert. You might spray late in the evening while the bees aren't active so the herbicide will be dry by morning. I would consult with a bee expert just to make sure.

Cultural Control: Removing Plants and Tubers Tubers are key to nutsedge survival. If you can limit production of tubers, you�ll eventually control the nutsedge itself. To limit tuber production, remove small nutsedge plants before they have 5 to 6 leaves; in summer this is about every 2 to 3 weeks. Up to this stage, the plant hasn�t formed new tubers yet. Removing as much of the plant as possible will force the tuber to produce a new plant, drawing its energy reserves from tuber production to the production of new leaves. Continually removing shoots eventually depletes the energy reserves in the tuber, because the nutsedge will have to use 60% of its reserves to develop the first plant and 20% for the second. However, mature tubers can resprout more than 3 times. Even though these newer sprouts start out weaker than the previous ones, plants can develop from them and produce new tubers unless you remove them. The best way to remove small plants is to pull them up by hand or to hand hoe. If you hoe, be sure to dig down at least 8 to 14 inches to remove the entire plant. Using a tiller to destroy mature plants only will spread the infestation, because it will move the tubers around in the soil. However, repeated tillings of small areas before the plants have 6 leaves will reduce populations. If you find nutsedge in small patches in your turf, dig out the patch down to at least 8 inches deep, refill, and then seed or sod the patch. Here is a link that might be useful: Nutsedge

Looks like what I've always called Jewgrass. Check out the attached link and see if you think it matches. Here is a link that might be useful: Annual jewgrass

It looks like you have a bermuda lawn. Do not use Roundup, it will kill your lawn. You can spray the entire with a broad leaf week killer. You can get one that attaches to your hose. You may need to spray it a couple of times. That will take care of the weeds that are not grassy weeds. For the grassy weeds it is best to prevent them with pre emergents. They are granular and are applied like fertilizer. If you are in N. TX then you will need to apply that on March 1, June 1 and Sept. 1. If you live in other parts of TX then check with your County extension agency for the proper dates. Keep your grass cut short, 1-1,1/2" . Taller grass will not be as thick. Mow low and mow often. This will help to thicken the grass. Fertilize once the grass start growing well, lightly every 4-6 weeks if you are trying to improve your lawn. Good luck!