The question was, if White can choose the corner (a8 or h1). Bh7 mates on a8. My maneuver starting with Bd3 regroups the pieces and forces mate on h1. => White can choose the corner.
Checkmate with knight and bishop in a specific chosen corner.

You, mean if the king does not run to the wrong corner? I don't know. I have no system. Somehow it will work out. I tried this endgame in two daylies, but I never had the chance to play this endgame against a human player IRL.
https://www.chess.com/game/daily/390489209
https://www.chess.com/game/daily/393527751

I think on lichess it is possilbe to try a blitz game.
https://lichess.org/editor -> "continue from here"
@MousamGoswami
Must admit I've never tried it, but I thought the Syzygy tables were principally designed for SF. I generally practice against Wilhelm/Nalimov but sometimes against unaided engines for a change.
For the KBNK endgame Syzygy and Nalimov are interchangeable because there are no pawn moves or winning conversions and an optimal mate will never reach the 50 move rule. They will give the same optimal moves.
For OP's endgame the tablebases are no use for the same reason that engines are useless to practise against. The tablebases can't change their spots either.

Well II'm the one mating, they are just trying to escape I tried lichess and chess.com and it was easy.
It is easy (whatever you play against) if you know how. Like anything.
Some things will try harder to escape than others and they tend to be the ones that know how you might mate. If they can't themselves mate then they also won't know how you might mate.
Lichess should be OK because they use SF14 and I think any version of SF at least from SF8 onwards will slip no more than two moves on the mates out of three games (as either colour).

1. Kf1 Kg3
2. Ke2 Kf4
3. Bg6 Kg4
4. Ke3 Kg3
5. Bf5 Kg2
6. Kf4 Kf2
7. Bd3 Kg2
8. Nd4 Kf2
9. Nc2 Kg2
10. Be4+ Kf2
11. Bf3 now black’s king is in a mating net. Kf1
12. Kg3 Kg1
13. Be2 Kh1
14. Ne3 Kg1
15. Ng4 Kh1
16. Nf2+ Kg1
17. Nh3+ Kh1
18. Bf3 mate
However, there must be a quicker solution when someone is using a computer program.

You can mate in the same color bishop corner, and if ur in the wrong corner u can force the opponent to the other corner
You can mate in the same color bishop corner, and if ur in the wrong corner u can force the opponent to the other corner
And if he's in the centre?
But the thread has gone well off topic. OP's question was whether mate in a pre-selected corner of the bishop's colour is always possible within the 50 move rule (presumably meaning from positions where mate is possible without any constraints).
You, mean if the king does not run to the wrong corner? I don't know. I have no system. Somehow it will work out. I tried this endgame in two daylies, but I never had the chance to play this endgame against a human player IRL.
https://www.chess.com/game/daily/390489209
https://www.chess.com/game/daily/393527751
Just looked at the game review on the first link. Interesting to see that Coach can't play the B+N endgame.
Coach tells @newbie4711 that his move 68. Nd5 is a blunder, though it's the only accurate move, and demonstrates it by first off blocking his own bishop with his knight, which should have resulted in a longer mate except he the makes his opponent walk into it with 70. Kf7 and then he apparently doesn't realise that he's set up for a quick mate at the end of his example.
Who coaches the coaches?
Against tablebases krbvkr is draw, of course.
The tablebases are not so dogmatic.
https://syzygy-tables.info/?fen=4k2r/8/8/8/8/8/8/R1B1K3_w_-_-_0_1
https://syzygy-tables.info/?fen=8/8/4r3/4B3/8/7R/2k5/K7_b_-_-_0_1
or more interesting (from the site)
@Ladyhawke79
To better illustrate what I meant about practicing against a human rather than an engine, I've played your position against SF14 aiming for mate on a8.
You'll notice that it's hardly different from a normal game. The engine makes no attempt to stay near h1 because it doesn't want to be near h1. It still thinks my objective is to mate anywhere - it can't change its spots.
But you could be struggling to do it within the 50 move rule against a human opponent.
I am sorry but I do have to ask, against a white Bishop would you wish to hang around H1 or A8? (I never got this KBN down myself) I thought the whole point of defense was to stay away from the mating squares. It is a question, I am not being snarky or anything.
You said you attempted to create a position so as to mate in the A8 corner, which you did. Are you aware after 8. ... Kb1, that instead of Nb3 had you played 9. Nc2 then black forced to
9. ... Kc1
10. Ba2 Kd1
11. Nd4 and now you are on your way to mate on H1.
@bigD521
OP's question was how to mate in a chosen corner of the same colour as the bishop, not either corner of the same colour as the bishop nor on a square adjacent to a corner.
For illustration I assumed the chosen corner to be a8 in the example OP had previously given.
With that choice, if I had mated on h1 I would have failed OP's task.
With OP's task Black's best chance to avoid being mated on a8 would be to first try to resist the advance of the White king towards h1 then drop back and hang around h1. If he's mated or stalemated in or around h1 he's foiled my plan, also if it takes me longer than 50 moves to extract him form h1 and force him to a8.
SF doesn't do that in my example because he doesn't know what the objective is. Hence the need to practice against a human who has been told the objective.
Many of the posts in the thread have, like SF, taken the task to be simply mate, so the thread's a bit confusing.
Well, I would start from this position. And it seems to be easy to regroup the pieces.
Bd3 is not he best move here (it wins in 20 moves with perfect play), Bh7 is the best move, it wins in 18 moves.
@newbie4711.
You don't say what you'd do if your opponent doesn't want to start from that position.
See my post here.