There are a couple of things to consider with this question:
First, training time can be a deceptive measure. Neural network training is considered "trivially" parallelizable. This means that the more computers you have access to, the faster you can train (most of the time, one computation doesn't depend on another, so you can do them both at the same time). Since the start of the current phase of self-driving cars, GPU performance has increased by more than a factor of 5. Further, large companies like Google have migrated to AI-specific ASIC chips. These are faster still. This means any estimate of "time" is likely to be confusing or misleading. The amount of time required to train a network has dropped rapidly over time, even if the number of processing cycles required has stayed the same.
Second, it is very unlikely that self-driving car companies have spent that time training a single model. Instead, they are probably starting from a given model (say, last month's), and trying different approaches to improving it, with new data, alternative training methods, or "expert" domain knowledge. This makes it difficult to reason about what it means to "get the results that are used in today's self-driving vehicles." If we count all the aborted attempts, probably it's on the order of high hundreds or low thousands of person-years of researchers (6-7 years, and there aren't thousands of people working in research in this area). If you also count related development and engineering efforts, it's probably an order of magnitude or more than that.
That said, it might be more interesting to think about the amount of simulated driving time that is needed to train a network in this way. As discussed in this excellent blog post, "Deep Reinforcement Learning Doesn't Work Yet", the amount of training experience required to train a neural net for this kind of problem is extremely large. To learn to play simple Atari games better than human players required about 244 hours of exposure. These games are typically just a single screen, and most humans can pick them up in a couple of minutes or less. This site estimates average time for a human to learn to drive competently at just shy of 70 hours. Applying the same ratio, we can infer that a deep neural net would want something like 2 years of experience driving to achieve human level performance. This seems like the right ballpark, but probably a lot of that driving is done "offline" in a simulated environment, rather than operating the vehicle directly.
Of course, these are just ballpark estimates. The exact figures are likely to be proprietary. Further, there are some reports that modern systems are abandoning neural nets, and moving back to a more "rule-based" paradigm because of the difficulties in training them. I'm not sure how much credit to give those reports, but it again makes it difficult to pin down a training time.