Rake it hard to remove the layer of thatch (dead grass) and expose the dirt in any areas that may need re-seeding.

If you have the time/cash rent a coring machine and run it over the yard - this aerates the soil and loosens it up so that the fresh seed will take root better. It also spreads around some grass that is rooted with the cores so your yard won't look as bare while the seed takes root. You can also take advantage of this to take a soil sample to your local extension office and find out if your soil needs any supplements like lime to help the turf.

Buy quality grass seed of the variety you want - you said Bermuda which is good for your zone, although it's a warm weather grass so it turns brown in the winter. You could get a mix of warm weather and cold weather seed so your yard would be green year round but that's up to you. I don't like mowing in the winter myself. Spread the seed. Don't bother with the stuff that has "fertilizer" built into it - that stuff's mostly filler.

Since you already fertilized this season you don't need to add any more of that.

Water sparingly once a week. Don't water more often or the grass will develop roots too close to the surface and will die if the heat gets too strong. A good way to know if you've watered enough is the tuna can test. Just
get a tuna can, which is 1” tall, (eat the tuna out of it, first) and
place it where your sprinkler is hitting. Run your sprinkler and see
how long it takes to get a half inch of water in the can – just like a
rain gauge. Usually it’s about 30 minutes. Depending on the severity of the heat and whether or not you get natural rain you should water between 1/2 to 1 inch per week. More than that can cause fungus and other diseases to kill your turf.

For Bermuda grass, set the height your mower cuts at anywhere from 1/2 inch to 2 inches. The longer you cut it the healthier it will be. Leave the trimmings on the lawn to shrivel up and compost it - if there are clumps that might kill the grass you can pick those up or spread them out so they won't. The trimmings provide the nitrogen and reduce the amount of fertilizer you need.

Here's a link for more info on growing turf in Texas: https://aggieturf.tamu.edu/texas-turfgrasses/

Leaving the clippings on the grass provides the nitrogen. No need for more fertilizer.

One of the most common mistakes people make is over-fertilizing their lawns. The run-off fertilizer is one of the biggest watershed contaminants in the USA. For Bermuda grass in Texas follow the directions at this link: Maintaining Bermudagrass Lawns.pdf

Please give some thought to the various turf builders and weed killers and chemical fertilizers and lawn care products your lawn is saturated with. Many of them contain ingredients that are hazardous to children and wildlife.

we have a 100% organic lawns and gardens. of which i am confident that my dogs and children are safe walking barefoot upon. i also feel safe eating the vegetables from our garden, also organically grown. Whenever i don't see dandelions growing in a lawn i inwardly feel a little sick.....This is the only earth we have! There's no do-over.

North Texas has clay soils, extreme heat and water rationing to make lawns challenging.
While I love Bermuda for barefeet, it is a maintenance nightmare. It can grow right under a two foot wide sidewalk in our warm almost all year soil just to strangled shrubs and gardens. Then it faints in full sun on triple digit days but doesn't like sun. I like the St Augustine in the mix of our yard but I bet those Aggies can suggest some native Buffalo Grass that is a better hybrid.
Get a mulching mower to leave most clipping for fertilizer. Bag it when leaves need raking and start a compost pile. In Richardson they will take them in compostable bags and you can go get free compost. Vacuuming the leaves out the lawn keep the grass from being smothered and makes a good mulch for shrubs and gardens.
In Dallas talk to the folks at Gecko Hardware for some more organic options and lots of fun stuff.
Good luck and Pray for rain without hail and wind.

oops I meant it doesn't like shade. no edit on tablet.