Two of us purchased a 2010 Hyundai. The test drive seemed okay. I
Just thought it was a bumpy few streets. Now after driving the car
Into the city, I realized these springs bounce way too much over the
Bumps. There's a 100,000 warranty on the car but no extra
Insurance. Is it too late to do anything about this?

If you bought the car new then take it back and explain it. See what they say. In new cars there shouldn't be a "bumpy" ride at all. Most new cars today ride smooth as glass.