Bearing in mind the OPs original question, it's not so much the key that's wanted as how to deal with the small deviation from the standard tuning.
Audacity can do this. It's not a particularly slick tool for the purpose.
The slickest way to do this, provided your ears can tell you how much out of tune you are, is to use either a standalone piece of hardware like a Korg Pandora PX4B (very reaonably priced 2nd hand on ebay last time I looked) and use the Aux Pitch function to adjust the song to the tuning of your bass. The pandora will go from in tune to (say) +1 semitone in 5 steps, so it will probably get close enough to sound in tune when you play along.
You'll probably get closer matching if you can find a software tool for the same thing. I use 'Vox' on the mac. I don't have experience with the others mentioned.
To do it with Audacity, first, import your song into audacity. Find a bit a of the song where there's one clear note sounding. Select that then choose Analyze, then Plot Spectrum. Then (and this bit is important) Choose Algorithm: spectrum, Size: 8192, Function: Rectangular window, Axis: Log frequency. And then put your cursor over the leftmost high spike in the graph. under the graph you should now see something like 'Peak 91 Hz (F#2) = -22.2 db' . (Ignore the similar bit of text that starts with the word cursor).
So the software has found your note(F#) and the exact frequency (91Hz). Now, you're set for adjusting the song. Finds the frequency F#2 should be from this chart
http://www.guitarpitchshifter.com/fig_2_1.png. We want our note to be 92.5 Hz. In Audacity, select the whole song, then from the menu, Effect, then Change Pitch. In 'frequency from' fill in the pitch from the song (91) and in 'frequency to' fill in the pitch you want (92.5) and hit OK. Now export the song as an MP3 and you can play along in tune.
Since Audacity's frequency analysis only gives frequencies in whole Hz, you get better accuracy by picking higher notes. And choose your sample carefully, you don't want to be frequency-analyzing the cymbals, or the bass drum,that won't tell you anything
So, you
can do it in Audacity, but if you can do it by ear you'll be much better off.