Question: Suppose both the kings are left in a fairly neutral positions with just rook at one side and a bishop at the other side. What is the outcome if both the sides play correctly?  

Can a side with only bishop claim a draw?

Related:

* [Rook vs Bishop endgame](https://chess.stackexchange.com/questions/37052/rook-vs-bishop-endgame)
* [Rook and bishop vs. opposite color bishop](https://chess.stackexchange.com/questions/23768/rook-and-bishop-vs-opposite-color-bishop)

Answer: 
See [Pawnless Chess Endgame](https://en.wikipedia.org/wiki/Pawnless_chess_endgame#Common_pawnless_endings_(rook_and_minor_pieces)) on Wikipedia:

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> Rook versus a bishop: this is usually a draw. The main exception is when the defending king is trapped in a corner that is of the same color square as [their] bishop (see [Wrong bishop#Rook versus bishop](https://en.wikipedia.org/wiki/Wrong_bishop#Rook_versus_bishop)). If the defending king is trapped in a corner that is the opposite color as [their] bishop, [they draw] (see [Fortress (chess)#Fortress in a corner](https://en.wikipedia.org/wiki/Fortress_(chess)#Fortress_in_a_corner)). See the game of Veselin Topalov versus Judit Polgar, where Topalov defended and drew the game to clinch a win of their 2008 Dos Hermanas match.
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Mate is possible, and the side with the Bishop definitely cannot claim a draw (until 50 moves is up).
The side with a bishop can't immediately claim a draw as there are opportunities for checkmate.

At lower levels, the defense isn't trivial either and it's in fact impossible if the side with the bishop can't manage to one of the "safe" corners (the ones with the color opposite to that of the bishop)