I see several use cases here:
- Bob and I, as a team, made, an effort.
- Bob and I, individually, each made an effort.
- Bob and I, as a team, made efforts.
- Bob and I, individually, made efforts.
after Bob's and my effort,...
seems to see all the effort (could be several actions) that went into it as one object, so seems to correspond most closely to case 1, but not the others. Case 2 is marginal at best, I think. Consider:
Bob put in effort on Monday. I did on Tuesday. After Bob's and my effort, the project was delivered.
This would be clearer with "efforts" or better rendered as:
after bob's effort and my effort,...
after bob's efforts and my efforts,...
because effort and efforts effectively mean the same thing, but it is a question of how the speaker views it. That's why case 1 could also be rendered as:
after Bob's and my efforts,...
If the speaker really wants to make the Count distinction:
after bob's effort and my efforts,...
after bob's efforts and my effort,...
Awkward, but precise and grammatically correct.
Case 3 and 4 imply that the efforts are being viewed as individual items.
after Bob's and my efforts, the project has been delivered successfully.
I think this is where the ambiguity is. I find it hard to distinguish cases 2, 3 and 4 with this example. Context is all that is left.
End result is effort works with case 1, efforts works with case 1, 3, and 4. 2 should be rendered differently.