I am confused, however, with Steve's comment in his Secrets to Stunning Wildlife Photography ebook that one has to have it in release priority with BBF as he states "if you have it in focus priority you won't be able use this method in a focus and recompose situation."
You really do want to set the camera for Release Priority when doing focus-recompose shooting in AF-C mode when enabled by setting up BBAF.
In some images you can get away with leaving the camera in Focus Priority mode but that's just lucky when it happens. Think of a situation where you reframe the image so the selected focus point is on your subject's eye and then you use BBAF to establish focus on the eye followed by releasing the AF-ON button and recomposing.
If it just happens that whatever part of the image (perch, bird's breast, other part of the animal, etc.) is in focus and under the selected AF point after recomposing and the camera is set to Focus Priorty shutter release then sure the shutter will still fire and you'll capture the image. So in that happy case everything still works.
But if after recomposing the shot the selected AF point happens to fall on something like an area of out of focus background and the camera is set to Focus Priority shutter release then the shutter will not release as that area is well out of focus.
So for general use of BBAF focus-recompose shooting you really want to set the AF-C shutter release set to Release Priority and not Focus Priority. And when running BBAF you'll always operate the camera in AF-C mode as there's no reason to run AF-S mode since you can achieve the same focus-recompose results via selective use of the back panel AF-ON button so single servo really offers no benefits when shooting with BBAF.
Realistically even when not using BBAF I'd always set AF-C mode up for Release Priority which happens to be Nikon's default for continuous servo mode as you'd generally use AF-C for action sequences where focus won't always be dead on but you still generally want to capture images as often the focus is close enough to make the shot useable during fast action sequences like birds in flight or running animals.
Bottom line, it's best to set the AF-C release mode to Release Priority and not Focus Priority when setting up your camera for BBAF.