We LOVE Blue Bayou and go every time we are at DL. We actually served the potatoes at our wedding because they are SO good.
While I really enjoy the ambiance of BB, a less expensive, less "special" alternative is Cafe Orleans. It is right across the "street" from BB and serves almost all of the same food. I know for sure that the Monte Cristo and Chicken Gumbo are the same because I asked the chef when I was asking for the gumbo recipe.
It's rather nice to sit out on the verandah and people-watch. The service isn't quite as good and the menu is definitely not as upscale but it is a good alternative and I enjoyed it. If you do eat there, don't pass on the Mickey beignets. They are faboo!