I only listened to the first recording. I thought, not bad, maybe about average for a performing band. Here's what I think you can do to improve, since you asked:
1) count off the tunes. I didn't hear the leader didn't do that and you all joined in roughly on time - but roughly is roughly and not crisp - and the tempo increased dramatically after everyone was in. Either the band leader needs to learn to count the tune at the correct tempo, or IMO, you'd be better served sticking with the initial tempo. Counting tunes is a skill that takes practice in my experience. I know I had to practice it.
2) get some lessons from a classical bassist. You're intonation is pretty good but your technique isn't doing you any favors. I think you'll find the bass easier to play and more fun with some good guidance on consensus technique - right hand down at the end of the bridge, full meat of the finger, left hand with intended shifts, good hand form, bass not so it's side is touching you full on, etc. If you really want to improve, start playing with a bow because that makes the intonation much easier to hear, assuming that you don't already.
3) add a bridge/solo to the piece to better engage the audience with the melody. I found the tune very repetitive the way it was and felt it could really use a "middle 8" or longer break.
Don't get me wrong, I don't think you guys are bad. In a bar, I'd probably leave because the band isn't anything special, but I can see lots of folks sitting through your set without complaint - of course, they've got a drink in their hand and a girl in their eye.