Bair out of shield is amazing, especially out of a shield pivot. You can somewhat treat it was Marth's Fair out of shield, given it's range and speed. I love to use it in Falco dittos. As the opposing Falco is laser torwards you, can you stuff out a Bair inbetween their SHL to Aerial approach (essentially the same way Marth Fairs).
The most popular options out of shield are definitely Shine and Dair. Never forget that Falco's shine is positioned around his body differently than Fox's / it does not reach out as much in front of him. Learn to shield DI moves inward to make shining out of shield easier / possible. Also don't forget Falco's retreating Dair can beat approaches such as Fox's SH Nair.
I guess this should be your general guideline:
If they are inside your shield with a non-laggy move -> shine out of shield
If they are inside your shield with a laggy move -> Dair out of shield
If they are not close enough -> wavedash or Laser
If they are approaching you with your back facing them -> Bair or reverse Laser (SH away, non fastfall rLaser)
If they are approaching you with you facing them -> retreating Dair or Laser (SH away non fastfall)