Puzzled by this question I did my own research and found numbers that allows to get a good comparison for year 2016:
According to the United States Parachute Association (USPA), there were 3.2 million jumps in 2016 and 21 fatalities. Therefore, the chances of dying in a single jump were 1 in 152,381.
For a comparison with driving, we can use data from the Insurance Institute for Highway Safety. According to which, in the United States there were on average 1.16 deaths per 100 million vehicle miles traveled.
Crunching those numbers, the chances of dying by driving one km are 1 in 138,103,448. Therefore, to equal those chances to one skydive you have to drive 906 km.
In 2016, a single skydiving jump in the US represented the same risk of death as driving 906 km (566 miles).
Many have pointed in that there might be an important component of the risk related with age, experience and how careful a skydiver is.
To approach to an understanding in that regard I've compiled the 147 fatal accidents in the USPA database that happened from 2008 as a result of solo jumps (i.e. not-tandem).
This data do not allow to infer real demographics trends, because I don't know how many total jumps were in each demographic group (I only know how many lead to a fatal accident). However, the visualization of some aspects of the data can be informative.
In the following figure each dot is a fatal accident, and it is plotted based in the numbers of jumps the person involved have performed before the accident (vertical axis) and the age of the person (horizontal axis).
It is clear that the bulk of casualties happen to fairly experienced skydivers (100+ jumps). So, as expected, the more you jump the more chances of dying you have. Note that the vertical axis is logarithmic (so to distinguish between people with relatively small jump counts).
This may lead to think that the first 100 jumps are quite safe, but we can not jump to that conclusion: If you check how many death are there for different jump numbers, you have the following picture
In this plot, the first bar counts deaths during jumps 1 to 50, the second bar for jumps 51 to 100 and so on.
So now it seems that most deaths are in the first 50 jumps. However, that does not mean that the first 50 jumps are more dangerous, because there were many more jumps corresponding to jump number 1 to 50 than jumps number 900 to 950. So, however informative, this have no real statistical value. And the trend suggesting that jumps become less dangerous as you gain experience might be just an artifact due to the fact that there are more beginner skydivers than experienced ones.