Nope. Kind of shocking how many people agree with this. A rotating schedule? What?
The other player is an acquaintance, not a friend, and pulling him aside to tell him that his boss said he plays like a robot and wants to fire him in lieu of yourself to "see how he feels about it" has no upside.
How the singer deals with the current bass player is between them, period; putting yourself in the middle is both incredibly unprofessional and may very well sour the singer on giving you the gig for creating needless backtalk and drama.
People lose gigs all the time, for a variety of reasons; if you take it personally to the point of bad mouthing your successors, you're in the wrong business and will quickly find yourself unhirable.
I think the number of people who agree with it are looking at the situation a little deeper than Darwin would.
I'll concede that the timing is an issue and OP should take a wait-and-see approach. But I stand by my reasoning that he sooner or later has to let the other bassist know he didn't intentionally target and sabotage the slot, that it was the BL's idea and she who approached OP.
Also, keep in mind they share a project at their church, OP referred to him as a "buddy" in the first post, and there is no doubt a church-folk standard and etiquette at play in this situation. I get the impression from OP that he cares about this person's feelings, and I personally respect that sentiment and believe it comes with some long-term benefits. Even if the other bassist gets fired and OP replaces him, OP has to face this individual on a regular basis. It's reasonable on his part to try to make things less awkward and as painless as possible.
It's not always a matter of tough luck, survival of the fittest. Like I said, I'd be excited at the prospect of working with this singer, but I wouldn't do it completely devoid of concern for the church buddy I replaced, and I wouldn't want him thinking I instigated his firing and backstabbed him.
I've never felt sorry for the bass players I've replaced. But I never knew any of them personally before I replaced them either. That changes things.
Also, you have to take a side-long glance at the BL. She has created an awkward situation. If she's going to fire her bass player, she had better do it soon and offer the slot to OP. If not, she's a loose-lipped turd-stirrer and I would be wary of her. I'd be letting her know I'm interested in working with her, but I have a relationship with her current bass player in another project and I'd like to do this as sensitively as possible without causing undue animosity.
When it's all said and done, it is up to the old bass player to suck it up and move on down the line. But there is no shame in taking his feelings into consideration and trying to think of ways to ease the blow.