Sometimes during the slower times of year you can walk up and get a table, I’ve done it before. But it is just so much easier to make priority seating reservations. You can call up to sixty days before your dining date at (714) 781-DINE (yes, I have it memorized).
BB is one of those places that is always going to be busy so it is really hard to suggest a non-busy time. I would say the best time to go would be a week day that isn’t during a school vacation. Also, if you chose a time to eat like 3:00 that isn’t lunch or dinner it may be a little less crazy than the normal eating times.
This is a bit late to be answering this question but here I go anyway. 1) I ALWAYS call in advance because IF there are any openings that day you want to eat there the spots are always gone 30 minutes after the park opens, so I would highly suggest calling in advance to make reservations. 2) The Blue Bayou is always crowded and popular, no matter what. When I went to DLR just last week the park was totally dead on Wednesday but the Blue Bayou was still packed, so make your reservations early if you can.