I went into a studio with another band for free just to get my name on the credits and a demo of my playing. They done a variety of originals with different styles, so that was a plus. The band has done nothing with the CD. They don't even attempt to push it or sell it off stage at band gigs. It turned out much better than I expected and was done by a studio pro with good credits. I don't know why the guy who wrote the music doesn't push it more? Too bad, a waste of time and money on his part. But works great for me as a demo of my talents. This was done by only one day in the studio, so it was well worth my doing it for free. You may want to consider such a barter with a guy writting original music. Worked good for me.....  

Speaking of which, did you contact that band you were interested in auditioning for?

A band I auditioned for about 2 years ago requested a demo prior to a live audition.  I simply sent them a 2 minute solo and a few clips of songs in various genres.  A little jazz, blues, metal, rock, etc, slow and fast.  I did not send entire songs, as they were not auditioning for a producer, song writer, etc...  Focus on what your strengths are, and be sure to include those examples in your demo.

Personally I had mixed feelings about sending a solo.  Most bands simply just want a solid rhythm time keeper.  Not a hot shot.  Auditioning with the attitude "how can I help," vs. "I am just what you need" will go far.

Good luck, and let us know how it turns out!