I've slowed down lots of bird song before but always had a problem getting rid of background noise completely. Now I've found a way to do it using the wonderful editing suite, PowerDirector 10.
Here goes: take your video clip into PowerDirector, then separate the video from the audio. (highlighted in blue)
Go to Edit Audio, and select Equalizer. This allows you to remove bands of frequencies at the touch of a button. Background noise is almost always at a lower frequency than the bird song so you just keep pulling down the slider till the noise disappears but the song remains.
But not quite. PD 10 only lets you slow audio to 50%. Save the audio clip and open it in the equally fantastic Wavepad Sound Editor (make sure you pick the free version) then slow the file to whatever speed and pitch you like. Save as a .WAV file and import back into PD 10. Then remove the old audio from the timeline and replave with the new. Stretch the video clip to match the new length (Powertools>Video speed) and you're done.
As you can see, the background noise in between the bursts of song has been completely removed.
And here's the finished result. At one point (28 secs) he manages to relieve himself while continuing to sing. A neat trick if you can do it.