Bit depth is a term that refers to: ability to capture audio or possibly a type of resolution.  A normal CD is at 16 bit depth.  There are 65,536 possible levels at 16 bit, and the number doubles with each extra bit up to 24 bit.  So you end up with like 17 million slices at that point.  Most people record at 24 bit and this is why its crucial to master and record at 24 bit, gives you a higher ability to record with more accuracy and detail.  Then you dither the audio at the final stage which is the process of keeping as much info of the 24 bits and putting it into 16 for playback. 

The other portion is sample rate.  44.1 is a normal CD, and that is basically taking a picture of your audio or sampling it at 44100 times per second. 

Its probably just a name, you can't actually play back a 2 bit file, it has to be 16. 

Example:

Uberzone's 4-bit (2-bit mix),  Just names or does it mean something?

Lots of producers use names of plugins, gear, distortion boxes, production lingo etc.  Dave is right though you can run lets say a drum part thru a bit crusher , most popular is probably 8 bit, but the final has to be 16bits.  Your just readin a title of a song like Uberzones Hamburger Bass mix... or 2 bit mix, doesn't mean much...or maybe its a clue to a secret treasure somewhere and he is saying take 2 steps back and start digging?

2 bit does sort of mean that...