I do not have any experience with Texas Bluebonnets, but in general any native plant's seeds can be harvested from the plant when they ripen and spread immediately in a suitable place for them to grow. I would watch the bluebonnets and you'll see seeds or seed pods develop in the places on the plant where flowers grew. These will probably be green at first, then slowly mature to brown and get sort of dried out. You can open a few along the way to check on the seeds. Normally seeds start out green or white and soft, then mature to brown or black and hard. When the seeds are dry and ripe, you can harvest them - usually they are ready to fall off of the plant when ripe. You can then simply spread them in the location where you want plants. The natural progression of the seasons will be enough to stratify the seed and it should sprout at the right time next year. I would expect a low percentage of the seed you collect to become plants, but since you should be able to collect a whole lot of seed pretty easily, that is OK. Like I said, these instructions are sort of general for all native plants, but I think they'll get you started growing bluebonnets. You definitely should not pull the plants, at least not until the seed is ripe. Once you pull the plants the seed will stop developing and unless it is almost fully grown, won't become viable seed. You shouldn't need to chemically scarify the seed - the ones that fall off the plant naturally sprout without any help. If you want to start plants indoors, then you might try to water sprouting method, but it sounds like you just want to sow seeds outside and hope for the best, so I wouldn't even bring the seed inside - I'd collect it and spread it at the same time.

bluebonnets are so easy to spread. The best way is to pull up the whole plant and just throw it where you want next year's plants to grow. It seems like you would be killing off next year's crop that way( in the original location), but enough of the seed gets self-thrown so that really doesn't happen. The bluebonnet makes a bean pod, you need to pull it up when it is dry but not so dry that all the pods have spilled seed. they do actually 'throw' their seed.

Put an armful of plants in one spot. The plant serves as a mulch to keep the seed covered. Germination of bluebonnet seed is low at the best of times but this gives me the best spread I've found so far: just throwing down the whole plant in a new location. I've seen a lot of people who mow the dried plant and rake the cuttings to spread a stand too.
j

Pick the bean pods once they turn brown and scatter on the ground where you want them. They should germinate in the fall.