I used this one, from time to time. It's nothing to do, one really have to wait before the sking grows back or calluses are built up again.
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But this is only a temporary solution. It's basically the same thing as newbie ballet dancers uses on their toes. It's the same when they do it too much and their toes starts to hurt. Beginners that is. Don't know what it's called. Even such professionals as old shred stalwart guitarist Steve Morse, couldn't do two gigs in a row, same night, because it's too tough on his fretting hand fingers. He had to wait until the skin grew back on his fingerpads on his fretting hand. No matter how much he was prepared, warmed up and relaxed. It had absolutely nothing to do with this. It's only the string bending and vibrato that the skin never gets used to. You flake some of the skin off anyway, now matter how much you've tried to hone it in by woodshedding for ages. I think it can be the same with the plucking hand of any bassist, really.
The real concession you have to make, which is detrimental to tone, is starting to play with a pick now and then. It takes some time to hone it in, and the timbre, tone is definitely not the same and you can't play all things with it. You may get away with some kind of hybrid picking with using your ring finger instead, but that takes even more time to hone in, and I've only seen 2 players pull this "hybrid" picking off sucessfully, also related to above mentioned Steve Morse: Andy West, and Jerry Peek.
But as everyone has said, easing off your attack, and carress your string, turn it up, use compression, don't lean in all of the time, and maybe as a last resort, use strings of lighter gauge or/and less tension. Flatwounds will be of great help too, but changes the sound way too much in a "muffled" and "muddy" direction if you should do some funky slap bass music too. Maybe bite the dust and start to use coated strings? D'addarios "half rounds" ?
You should "moisture" your skin on the fingerpads after each gig, if it turns up so dry that you'll have cracks in it, that will crack open and start bleeding. Band aids will only help that. Or simply put: I think you're playing too much, actually. Don't use chalk baby powder to dry up your hands prior to gigs, if it's outdoor in a humid summer environment. Some do this. But it's detrimental and will only worsen the drying up and cracks.