Don’t offer yourself for the band. That’s a faux pas, in my opinion. If someone came up to me being like, I would like to replace your bassist, I’d be like, go get lost.
However, do go introduce yourself to a band member or two and let them know that you have an interest as a musician to play with them and you play bass and you like their style and you’re serious. That’s how my band got our last drummer. He didn’t know that the spot in my band was about to become vacant, but he offered that he’d love to connect with me in a future project. One day later, I was like, so about that thing you said yesterday....
However, do go introduce yourself to a band member or two and let them know that you have an interest as a musician to play with them and you play bass and you like their style and you’re serious. That’s how my band got our last drummer. He didn’t know that the spot in my band was about to become vacant, but he offered that he’d love to connect with me in a future project. One day later, I was like, so about that thing you said yesterday....
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I'm broke enough as it is, your gig is safe!