How big are the bare patches? Could you start the seed as "plugs" and then plant those instead of seeding in place? This technique would work well with a species like buffalo grass (Buchloe dactyloides) which will send out stolons and colonize a larger area than a bunch grass like little bluestem or a grama. Though, its not an overly agressive grass so it wont take over like Attila the Hun.

You can of course do the same with a bunch grass, start it in a container and plant it out once its is larger. By doing that you will have better control over germination conditions and the plant will be more robust and better able to compete with the existing plants. It would be helpful to know what species of grass you have there though because in some cases they might simply be too much for many native grasses. Smooth brome (Bromus inermis) for example is an rhizomatous grass species that creates a dense sod which will choke out pretty much anything you try to plant.

Grass is not broadcast seeded. You don't get the right seed to soil contact for it to germinate well and it will likely just blow or wash away or be eaten by birds. Instead it is either drilled to the proper depth or spread into a soft, prepared seed bed and "raked in" to cover the seeds and a roller than used to ensure good contact. Making sure that the seeds remain wet (they are only planted about 1/8" deep) up to, and even for a while after, germination is crucial. That is one of the biggest causes of failure when reseeding a lawn or a restoration site. Mulch is infinately useful. Depending on the size of the area you can use burlap or something similar (the seedlings will grow through it and it will decompose on its own) or a loose application of straw. Wheat is an annual so any plants that pop up won't really cause a long term problem. We even used it as a cool season cover crop in our restoration areas on occaision. I wouldn't use grass hay since its typically full of weed seeds and the grasses used are often exotic species that you probably don't want growing and crowding out your natives.

Given water and warmth grass seeds germinate readily and easily. They don't require cold treatment (stratification) or keep you waiting for weeks while water tries to enter a tough seed coat. But if that top layer of soil dries out, you're in for a lot of frusteration. If you don't live in an area that gets enough rain to keep the soil wet or you can't irrigate, I don't think you are going to get the results you want, especially just throwing them out and letting nature "take its course" so to speak.