Traveling from El Paso, TX, to Tulsa, OK? No ID, but traveling companion has one

It seems you want to travel by bus. Greyhound has a mechanism called a "gift ticket order" where your aunt can purchase tickets for you, and you can pick them up by giving only a password, no ID required. We have an answer all about that here, and you can contact Greyhound for specific assistance using their website to book tickets.

To answer your further questions, it looks like bus tickets for two people from El Paso to Tulsa will cost around $168/person for a round-trip if you book in advance. You'll need to search on their website for the exact price, as it depends on what days you want to travel. The trip will also take 16-20 hours each way and requires several transfers.

In contrast, a flight will cost more like $340/person for a round-trip, but prices vary significantly depending on when you want to travel, so you'll have to search for that yourself. To fly, you will need one of these forms of ID, however. But if you're eligible for an ID and are able to get the required documents together, you could get an ID, which would be useful in many situations.

If Greyhound is too expensive, you could perhaps find someone who happens to be driving that way and is willing to take passengers, possibly for gas money, on a website like Craigslist.