"Shy Man"

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A: Thank you for arranging such a party like this today. I really enjoyed it!

B: Did you talk to everybody?

A: Yeah, except one guy who seems so shy. Who was he?

B: Oh, he is a new member to our community. He told me "I am a bit shy in nature so please forgive me if I give a bad impression at first." I think he is just nervous among unfamiliar folks. 

A: I see. Hope he gets used to it soon!

. . . Then time for the check. 

People split the bill and paid their own. The man in question was not able to pay his, because he was also shy with this.

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In the nonsense story I made up, I wonder how an adjective "shy" develops into the sense of "lack in the amount of money."

OED defines this "shy" as one of the transferred uses of sense of timidity, recording the first use in 1895, in which the sense of shortage appeared in the context of betting: "to be shy a dollar in the pool"

It's interesting to observe the way the original sense of word develops and transfers in various ways. As for "shy," it's easy to imagine the situation in which "shy" is applied to the sense of "lack" when people, diverting themselves with betting, shout to others "don't be shy! Pool!", out of which the meaning of "shy" becomes common.