You got this. And I have an example to show that!
I just played 47 covers Saturday at an outdoor festival; after getting a call from another bass dude that was supposed to do it; that a "new" band needed a guy, but he couldn't fill in, big issues with his father's health. I got that call on Thursday mid-morning.
55 hours until showtime!
I'd only actually ever played a dozen of the songs live, and there were 25 that I wasn't familiar with or even not have ever even heard before. OK, I'm a moron but I took it. Here's why.
"New", as in lead by a just-turned 16 yo guitarist/singer/prodigy kid, Hunter. There was also a good drummer, Mike, that was about 33, and the kid's mom Heather on about 1/8 of the song vocals, great voice. Mostly old and rock-ish blues, and 'outlaw' country (Johnny, Willie, Waylon and both Hanks) and some southern rock and some pretty hard classic rock, and 60s=70s hippie chick pop songs. The kid is amazing, sounds like any of those deep voiced folks, shreds like you wouldn't believe; strums well, cavorts around on the stage; fearless. Hates modern music. Nice kid, too, and very supportive family.
I told him I just wanted to make sure I got an invite to his First Grammy party 10 years from now. He thinks I was kidding. I am not.
It turned out I really had heard 12 of the 25; so now I'm down to 13ish insurmountable problems. Thanks mom and dad for playing all that country and blues stuff in the 60s at home. Break things down into what you already know, they aren't a problem!
Anyway, the blues weren't a problem, and surprisingly neither were many of the country and rock tunes. Blues I know. Walking and bouncing the 1-5 will get you through almost all of the country. That was a start.
First, listen to each song you don't already know well, undisturbed, try to start picking out the chord pattern, and see if you can specifically notice where things are like bridges, breaks and key changes (we had 7 of those and I only missed one, temporarily.) Fortunately I had the info on what key everything was in.
Listen for the bass "hooks" and learn those, otherwise just make sure you know the chord pattern for each song.
Then play along with them a little one at a time just to get the "gist" of each song, the feel of it.
This is where you steal stuff from yourself and any other bass player you can think of; there's only a dozen notes, really, all the combos have been hit at least once or twice, at least the good sounding ones. Just pick whatever you can think of that most fits.
You are going to practice with the band, right? You're ready. NOTHING is better than playing with live musicians!!! We had 3 hours together that Thursday night, got about 1/3 of the way through (I was still on the 25 number until then, finally figured out the 13 after practice that actually needed work.) 47 to 13 in three hours. Yeah, I'm still fearing the worst, but not as much.
The next thing; sit back and listen to them again. Do that frequently, you have time. It DOES add value, lots, but it just doesn't seem like it, it almost feels unproductive. Play through them again, but more intently. Then go goof off and let your subconscious work on it.
Saturday early afternoon we got together for another couple of hours just to go over the few I had problems with and the female singer tunes. Another practice for you.
That's about it; the bridges, breaks and key changes WILL screw you up if you let them, don't. Watch out for the verses or choruses that pop up to the 4 instead of starting on the 1. The rest, if you know the chord patterns, is just playing along and having a good time.
Saturday night was great! The nerves left after the first three or four songs. Yeah, I told them to expect it, and I flubbed up maybe 6 to 8 songs a bit (I told them half!) until I caught on to the chord progression, but basically that's about it. The half-toasted fest crowd didn't even notice. The drummer made things really easy, very steady and easy to groove with. The kid was on fire what an inspiration! Mom did good, I even had backing vocals/harmony for most of her oldies (Big Yellow Taxi, Son of a Preacher Man and a couple more.) We even did an original on the fly; he told me the chord pattern and away we went, I think even he was impressed. Thanks again Mike drummer guy.
What a blast, never thought I could do that; hey, you never know until you try, but you never know unless you try either!
Edit: I slept 16 hours on and off Sunday, still can't believe it. And yeah, you'll do great, too!