What the OP is describing is definitely not bump steer, it's death wobble. Pony Tail has a pretty good video on YouTube on how he fixed his on a 2021 JL. His is pretty mild and sounds like what the OP is experiencing. Obviously, I can't leave a link or even mention his name. Search for...
Sounds like the start of death wobble. Something is loose on the steering and/or suspension. It will most likely get worse as time goes by. Check the torque on all the bolts on your suspension, particularly the track bar. That's a good first step.
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I will drive a little bit to meet someone, located near Savannah, GA and I-95
You know Aldo, my orange Jeep has 92,000 miles on it and drives better now then when i drove it off the lot...seriously. All you need to do is upgrade every single steering component on the vehicle (except the steering wheel).