user16501: I am playing with only a bishop (black squares) and king vs a lone king.
Is it possible for me to win?

user12523: No. Even if you got your opponent's king to a corner and checked it with your bishop, your king can control only two of the three flight squares.
The most you could achieve is a stalemate, if your opponent helps. Therefore king and bishop vs king is considered a draw by insufficient material ("dead position" is the term used in the FIDE Laws of Chess; see article 5.2.2). 

16501: <p>I am playing with only a bishop (black squares) and king vs a lone king.
Is it possible for me to win?</p>
 12523: <p>No. Even if you got your opponent's king to a corner and checked it with your bishop, your king can control only two of the three flight squares.</p>

<p>The most you could achieve is a stalemate, if your opponent helps. Therefore king and bishop vs king is considered a draw by insufficient material ("dead position" is the term used in the <a href="https://www.fide.com/fide/handbook.html?id=208&amp;view=article" rel="nofollow noreferrer">FIDE Laws of Chess</a>; see article 5.2.2). </p>
