I had a 135mm L attached to my 5dIII, ISO 160 (was set on Auto), f/8, 1/125 (was set on Av, forgot to change it in the haste). Thanks in advance.
You simply were not going to get close enough with 135L to fill the frame with the bird without scaring it off. At least 300 or 400 mm would have been nice.
I have one of my C1-3 custom settings set up for exactly situation like this, including Al servo, burst shooting mode, shutter priority with high shutter speed for moving objects.