The main character of Saki's short story "The Storyteller" is the young bachelor who is travelling in the railway carriage and has to share such carriage with a lady and three children. The lady is the children's aunt and she is apparently unable to take control of them, for which the bachelor is extremely aggravated.
The physical description that is provided of the bachelor is not sufficiently detailed, but the reader can infer from the expressions that are described coming from the bachelor what he must have looked like to the aunt.
Saki narrates how the bachelor had a frown and a scowl that made the aunt perceive him as a "hard, unsympathetic man". Other than this physical trait, Saki does not expand on the bachelor's physical appearance at all. We know that the bachelor's personality was entirely amiable for the children, because he complimented, entertained, and left a great impression upon them. The aunt was never pleased, especially when the bachelor pointed her inability and heightened his own ability to keep the children quiet.
Therefore there is no official description of the main character simply because the bachelor's story would have been interrupted by Saki's intervention as an external narrator. Instead, Saki allowed the internal narrator, the bachelor, to control and move forward the plot of the story.
As for his psychological description, the bachelor is a man whose situation as an unmarried and disengaged society gentleman has rendered him free to move about freely and quietly. This is evident in the way that the aunt's consistent nagging as well as the children's bad behaviors seem to cause him much grief.
Interestingly, however, the bachelor seems to take sides with the children, for he volunteers to tell them a story which is both creative and entertaining. This means that the bachelor must have an inner child-persona which may have been as mischievous as that of the children; hence he dislikes the aunt probably as much as the children dislike her themselves.
The fact that the bachelor makes such a good impression upon the children tells the reader that he must have been charismatic, eloquent and easy to understand. Therefore, we can conclude that the bachelor is essentially a child at heart who also wishes to get back at the aunt for her constant nagging.