Consider the following position:
What are the possibilities for checkmating the white king within 16 moves?
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When I put the black K at h1, which seems fairly worst-case, Stockfish says mate in 16. This doesn't necessarily mean it's the fastest way, or even completely accurate; chess engines without end-game tables can be very awful.
Here's the solution. Good chance of being accurate ;-)
[FEN "3K4/8/8/8/3b4/3b4/8/7k b - - 0 1"]
1. ... Kg2 2. Ke7 Bc4 3. Kd6 Kg3 4. Kc6 Kf4 5. Kd6 Bf2 6. Kc6 Ke5 7. Kd7 Bb5+ 8. Ke7 Bh4+ 9. Kf7 Kf5 10. Kg7 Bg5 11. Kf7 Bf6 12. Kg8 Kg6 13. Kf8 Bg5 14. Kg8 Bh6 15. Kh8 Bg7+ 16. Kg8 Bc4#
Again, I started the black K on h1.
I am not surprised. Consider that the K needs 8 moves to get all the way across the board. The adjacent bishops might need 8 more. That's 16, so 9 moves remain for rearranging pieces. No sweat. B+N is harder.
This likely is not the answer you are looking for, but Jerry (A 2200+ USCF National Master) from the Chess Network has a nice video explaining the algorithmic approach to checkmate with two bishops. I think it solves your problem in less than 25 moves.
Endgame tablebases, which you can find at this website, will assure you that there is no placement of the Black King such that White can hang on for longer than sixteen moves if given the right to move first.