The EXIF data is in the picture. Bokeh is almost unavoidable when shooting at 600mm and reasonably close subject. These are great images of this beautiful bird though, so there's that.
I think my 600mm would show you nice bokeh is readily avoidable. Mines a mirror lens & the doughnuts can be very distracting...
I understand the "doughnuts" you speak of are more profound in some lenses than others. Bokeh [simply] is a blurred background caused mostly by shooting zoomed in with a telephoto lens with a close[r] subject. Supposedly, better lenses give more of the points of lights "doughnuts" you speak of. It's the blurred background that I think is hard to avoid. I don't know how to avoid the "doughnuts" if your lens gives you them but none of mine give those circles of light. Most people consider them a feature rather than something to avoid. I particularly like the subdued "doughnuts" in the OP photo's rather than the harsher ones some photo's have.
Personally when I want a blurred background and my photo doesn't have it, I do it in post. Particularly useful when the background subtracts from the photo.