I put mine on one of these: https://www.uhaul.com/Trailers/Auto-Transport-Rental/AT/
And towed it behind one of these: https://www.uhaul.com/Trucks/10ft-Moving-Truck-Rental/TM/
While living on base you can bike to work. I know two IPs that did that. Have fun when the afternoon storms come out of no-where. Off base? Best to have a car or live with/down the street from a classmate. Once you get off formal release you guys will probably want to leave base at different times though.
Not sure about the Uber situation in C-bus. Wasn't around when I went through. Taxis were pretty much non-existent. As far as one way rental at the airport, you will have to call the individual rental car companies and ask. Probably not many people here will have info on it cause probably 95% of us drove/had cars at UPT. I didn't know anyone while I was there that didn't have a car. IF there is a rental car company downtown that is also at the airport, I am willing to bet my paycheck the rental car company is about halfway between the airport and the base. Might as well get an uber the whole way to base, especially since the AF is gonna pay for it. Because once you take the rental car back downtown, you still have to get back to the base(about a 15 minute drive). So I hope you know someone down there or can make friends real quick with someone that will drive you back.
Honestly I don't know why anyone would turn down a paid road trip. AF only wants you driving max like 6-8 hours a day or something like that. Will even pay per diem rates for the hotels along the way. Spend the night in Flagstaff or Phoenix check out the sights, another night in Amarillo, OKC, Memphis. Or pick a different route with different cities, spending a night at each one.
Buying a car in Columbus, there are plenty of dealerships and used car places around town and in Starkville. Easy to get rid of? I put my car on Craigslist at 11 AM and sold it 8 PM. Internet is a beautiful thing. You could put it in the lemon lot on base to try to sell it as well.