Except for truly prodigious learners, really ingraining the material takes time (not simply the time working on the task, but time elapsed since the work began), which is essentially memory and neurological reorganization. You're right to try and master five for the audition, and tackle the rest as you go along. I would make them prioritize the list for you...they get what they want, and you can create a hierarchy in your mind. I'd also ask if there's a particular setlist order; if there really is, learn them in that order. If you can, run through increasingly longer playlists, bass in hand, from song to song, without a break, just like on stage. Don't agonize over blank spots; keep moving and get chunks of material. Focus on particular songs and passages that are truly difficult, but you know you have to fill up the whole void, and it's not likely to be perfect for a while. Roll with it.
If you don't read charts, and they don't write them, your tabs are a good thing (IF) you actually are a visual learner, so you get cross-referencing of the material in your mind. If you find you're really all aural, maybe just a list with the key of each song is better than partially reading a chart. Use your knowledge of your own learning strengths regarding charts.
I always immerse myself in a band's material, at the gym...in the car, every trip...every chance I get, to ridiculous repetition. I don't listen to anything else if there's a time crunch. The only missing link there, is that the cues you get from the recordings are often very subtle, and they're missing or altered in the live setting. If possible, drilling yourself on the chord arrangements helps out in this area; if you simply don't hit clunkers on the one of a chord change, you're avoiding the biggest land mine. Everybody knows how awful it is for a bassist to hit a wrong note. We're not allowed.
Fun, isn't it?
Good luck!
