As Nickさん said,「速い」is used to mean "fast" in terms of speed and quickness, while「早い」is used to mean "fast" in terms of something being early or soon.
They both have very similar meanings, but have a slight nuance to how each is different. It also doesn't help that, for quite a few sentences, either can be used and still make sense, but it would have a slightly different meaning.
While they both generally translate to "The bullet train is faster than the car", the sentence with「早い」could potentially also mean, "The bullet train was earlier than the car", depending on the context. It could be that you were waiting to see which arrived earlier, and would just take whichever came first.
I hope this helps, and please do not hesitate to ask if you have any other questions.