Comparing the etymology of similar words and looking at their other uses are both good ways of working out the difference between them. If you look at the etymology of 'bewilder', you'll see that it means 'lead astray'. So if you are bewildered, it is like you are wandering hopelessly in the wilderness, with no idea of where to go or what to do. A baffle is an obstruction of some kind which prevents flow of movement. If you are baffled, you are stuck. There appears to be nowhere that you can go and nothing that you can do. If you think of these two images, they are opposites in some ways. However, the meaning is the same : you are confused and don't know what to think or do.

I am baffled and bewildered by the meanings of these words! They mean the same thing - you can use whichever one you feel like. To me, there is only a slight difference in nuance - I feel that "baffle" is more surprised and maybe implicates a lack of information. "Bewilder" is more utter confusion, and they don't know what to do. So when the police run out of evidence, for example, you would see "police are baffled" in the newspaper, but never "police are bewildered", because it would imply that they don't know what to do. I hope this helps!