As the subject says, I am a bass player and I am trying to learn some passages in a few songs I have. Is there a way that I can cut out the bass (similar to a vocals cut I keep reading about) using audacity?
Cutting out the vocals only works if the vocals are dead center of the stereo mix - even then, any stereo reverb will still remain. The so called “vocal remover” just removes audio that is identical on both left and right channels (which is sometimes the vocals).
Unless the bass part is positioned dead center in the stereo mix, you can not remove it that way. The best you can do is to reduce the appropriate bass frequencies with the Equalizer effect to make the bass a little less prominent (you will still hear it though, probably quite clearly).
<<<The so called “vocal remover” just removes audio that is identical on both left and right channels>>>
The Audacity version of this tool is called the “Center Pan Remover” for a reason. That’s more like what it actually does. Anything dead center in the middle goes. Lots of times, they put the bass performance in the middle, so you may luck out.
Center Pan Remover (Voice Remover–Search the page for “Center Pan Remover”)
http://audacityteam.org/download/nyquistplugins
<<>>
Please note that we throw the word “Stereo” around a lot. If the performance is in mono, or even stereo with the same thing on both tracks, you’re dead.
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That’s not entirely true, either…
Voice Isolator (Opposite of Center Pan Remover)
Voice Trap
http://www.cloneensemble.com/vt_main.htm
Extra Boy
http://www.kvraudio.com/get/1651.html
One of these programs will do both isolation and removal, and it has tools so the target performer doesn’t have to be in the middle. I’ve never used it. I have no idea if it works or how well.
Koz
Tut tut koz, quoting me out of context 
(referring to using the “center pan remover”)
You can in fact remove a mono part from anywhere within a stereo mix, except for extreme right or extreme left. However you cannot do it automatically with the center pan remover (the clue is in the name).
How the “center pan remover” works: A stereo signal is essentially 2 mono signals, one for the left channel, and one for the right. Anything that is dead center will be identical in both left and right channels. The center pan remover, “inverts” (turns upside down) one of the channels, then adds the two channels together. Any signal that was previously identical in both channels, is now equal but opposite (equal in amplitude, but 180 degrees out of phase) and will be canceled out.
This process is quite easy to do manually, by splitting a stereo track, converting each of the new tracks to mono, inverting one of the new tracks and then mixing the two tracks together as a new mono track.
Now let’s consider if there is a mono source (a bass guitar) that is panned 50% to the left in our original stereo mix.
Start the same procedureby splitting the stereo track - at this point you will notice that the mono source that we want to remove (the bass guitar)is louder in one track (previously the left channel of our stereo track) than the other. Now convert both of the new tracks to mono, and invert one of them. If we play back our 2 mono tracks at the same time we will notice that the bass guitar that we were hoping to remove is still present, but at a lower level. However if we reduce the level of track with the louder bass guitar by just the right amount (in this case -6 dB) then the bass will disappear completely.
Yes it’s a lovely theory, and it does work provided that the bass was a true mono source within the mix. Any natural reverb of that bass in the recording, or any stereo effects applied to the bass, will spoil it for us.
Re. Voice Trap / Extra Boy:
I think several of us would be interested to hear how well these work 
thanks to those who posted their advice above. It will really help me.