Although their driveway was what caused the damage, it is the driver's responsibility to navigate slowly over bumps to avoid damage. So, in this case, the owner of the driveway wouldn't be considered at-fault or responsible for the damages. What I do recommend, however, is getting an estimate for the damages prior to speaking with your insurance company. In our State of Insurance Analysis
in 2016, at at-fault accident (which this would be considered if you filed a claim), raised premiums an average of $539 a year in South Carolina
(58). Now, for most claims you will be charged/rated for 3 years. So that $539 will stretch to $1,617 over time (on average, estimated). If the estimated amount of the damages caused the driveway is greater than that $1,617, you might consider filing a claim. Otherwise, your best bet is to handle this out of pocket.