Old Bryson is one of the middle-aged men who frequents the gentlemen's club to which "Young Gillian" also belongs. Below, I listed different character traits and explanations of why he fits those descriptions.
Bryson's temperament is that of a curmudgeon. For, besides generally desiring to retreat from others with a book, Old Bryson seems uninterested in those around him and appears to be a person of fixed ideas. In short, Old Bryson is a misanthrope and a cynic.
So, when Gillian enters the club and approaches Bryson, who is well sequestered from the other men, Old Bryson "sighed, laid down his book and took off his glasses," knowing Gillian will force him into conversation. Gillian tells Bryson he has a funny story to relate. Bryson's only reply is that he wishes Gillian would relate it to someone in the billiard room, where the other men of the club are congregated.
"You know how I hate your stories."
"This is a better one than usual," said Gillian...It's too sad to go with the rattling of billiard balls. I've just come from my late uncle's law firm of legal corsairs."
Gillian tells Old Bryson that his uncle has left him $1,000 and he must spend it. Bryson observes "the late Septimus Gillian was worth something like half a million." Gillian tells Bryson that his uncle left most to science and the rest to other people who worked for him. Gillian then asks Bryson what he should do with this $1,000.
With one thousand dollars, Old Bryson tells Gillian dryly that one man could buy a home, while another might choose to send his wife to a warm climate to heal. He continues his air of superiority until Gillian stops him.
"People might like you, Old Bryson," said Gillian, almost unruffled, "if you wouldn't moralize. I asked you to tell me what I could do with a thousand dollars."
Clearly, Bryson enjoys taunting Gillian. Now, he says sarcastically as he laughs dismissively,
Why, Bobby Gillian, there's only one logical thing you could do. You can go buy Miss Lotta Luriere a diamond pendant with the money, and then take yourself off to Idaho and inflict your presence upon a ranch. I advise a sheep ranch, as I have a particular dislike for sheep.
Since it is obvious that Old Bryson wants Gillian to leave him, Gillian thanks him, saying Bryson has hit upon "the very scheme." He tells Bryson he always knew he could "depend upon" him. Gillian leaves in a cab.