Catalysis of the reaction: N-benzoyl-4-hydroxyanthranilate + S-adenosyl-L-methionine(1+) = N-benzoyl-4-methoxyanthranilate + S-adenosyl-L-homocysteine + H+.
S-adenosyl-L-methionine:N-benzoyl-4-O-hydroxyanthranilate 4-O-methyltransferase activity