I know that flying with a bass tends to be very taboo, but I'll offer my experience as I never experienced any problems:
I've flown with American Airlines, using a friends old Gage flight case, a few times. One time when trying to check it, they gave me a bit of grief at the gate until I finally had to show them their own policy that revealed that yes, they could in fact check the instrument. Have fun getting all the weird looks from people as you walk your bass around!
And yes, you do have to check it. I think even if you buy a seat for the bass, the airlines won't let you bring it in. Tubas and cellos though are allowed.
Anyway, every time I checked my bass they didn't allow me to be present for the TSA inspection, but I packed pretty clear instructions in the case for how to repack it. Every time, it was repacked properly. My bass was never damaged, and it was never lost in luggage (although I do suggest putting an airtag or similar device with your bass). Other than the physical struggles of hauling a flight case around, I experienced literally zero problems.
I will note that it was very expensive to check the bass, though. This was in 2023/2024 and it was always $200 each way. I think other airlines are similar now.
I think considering you're going from Texas to Chicago, driving is the best move since it's not that long of a drive, but I do want to point out that there are lots of bassists who fly with their instrument regularly for auditions and experience very little issues, and many of them fly with very valuable instruments. Really, the only thing that should deter anyone IMO is the cost of checking it if it's not a removal neck instrument.