Several people have asked me this question over the years, so I'll give you an answer that applies to ALL my photographs. I don't ever remove the backgrounds in my images using software - the soft, blurred backgrounds are the result of the lenses I shoot with and the way I position the background.

Lenses
I try to stick to lenses with either a long focal length or wide aperture as both these factor into getting a shallow depth of field. My lens of choice for bird photography is the Nikon 400mm f/2.8 VR used mostly with a 2X teleconverter, and for flight shots or very close subjects I use the Nikon 70-200mm f/2.8 VR (sometimes with a 1.7x teleconverter). Both these lenses have pretty nice Bokeh, and using the teleconverters further reduces the depth of field compared to a 'straight lens' - for example, the 400/2.8 with 2x teleconverter (effectively 800mm f/5.6) has a smaller depth of field than a straight 800mm f/5.6 lens.

Background positioning
I try to make sure the background is as far away from the subject as possible, as combined with a small depth of field this results in a blurred background. How can you change the distance of the background in wildlife photography? Simple - just reposition yourself so that there's nothing behind the subject for 10-15 feet at least.

An example of good Bokeh - the background is a blurred, soft wash of color and emphasizes the subject


Bad Bokeh - the branches in the background detract focus from the subject