Okay, so after hearing some European guys badly butcher the word "bayou", I feel the need to educate some folks. I don't know if I just find it silly because I'm a southerner and live near enough to bayous to take them for granted, but I find it hilarious and annoying at the same time that nobody knows what a bayou is.
A bayou is a low, slow-moving body of water. Much like a swamp, but more like a very large, shallow lake. Bayous are common in Mississippi and Louisiana. Go find out more about bayous on wikipedia.
Now, for the pronunciation. Wikipedia says it is pronounced /ˈbaɪ.oʊ/ or /ˈbaɪjuː/. But for the non-linguists among us, that isn't very informative. I pronounce it by joining the sounds "bye" and "you", with the emphasis on the first syllable. But probably the best way to tell you how to pronounce it is to demonstrate how people FROM bayous pronounce the word.
And so, I give you this video. For the relevant bits, go to 1:08 in the video. He is singing "Born on the Bayou".