I would lean towards shocks or suspension issues in general. You might try pushing down on vehicle and if it continues up and down more than once, you likely have bad shocks, however I would go to a shop that does suspension work and have them check it.
The mileage can be irrelevant depending upon how the vehicle was driven by previous owner and the surface conditions that it was driven on. 'Catching air' 1 time can ruin shocks, suspension, etc., as an example...
What will you do if you replace tires and same thing starts happening again?
I would seriously get the suspension checked and perhaps research having the tires trued before buying new tires. JMHO
Good luck!
