I need a good bibliographic source (preferably a book) about the following.

After knowing the value of his autograph in the London market, Bernard
Shaw started to write checks for smaller amounts telling the
beneficiaries the advantage of not collecting them.

Here is a good journalistic source that I hope will meet your needs:

"Shaw's popularity often puts him in the most embarrassing situations,
despite the fact that he leads a quiet private life. Like all good
citizens he pays his bills in the orthodox manner by check. Last year
he sent to the bank for his pass book to determine his balance and
discovered that for over three months no checks had been presented to
the bank for collection. Tradesmen had been selling the checks for
Shaw's autograph and were obtaining more than the face value of the
check."

The M.I.T. Tech: Friday, December 12, 1930
http://www-tech.mit.edu/archives/VOL_050/TECH_V050_S0340_P001.pdf

One reason for the high value of Shaw's signature is that Shaw scorned
autograph-hunters, and was disinclined to gratify their requests.
Although his secretary sometimes took pity on autograph hounds, Shaw's
own response was a printed card saying this:

"It may interest collectors of autographs to know that Mr. Bernard
Shaw does not regard requests by strangers for his signature as
legitimate collection. He signs enough genuine documents every day to
give collectors ample material for the proper exercise of their
peculiar industry. His secretary has instructions to return all albums
and refuse all applications which ignore this distinction."

Brown University: The Quintessential G.B.S.: Correspondence
http://www.brown.edu/Facilities/University_Library/exhibits/shaw/correspondence.html

You may be interested in a story that is often told about Pablo Picasso:

"Pablo Picasso famously told people who interviewed him that people
didn't buy his paintings. What they were actually buying was his
signature. This was true: What would the same piece of art be worth
had Picasso not signed it? It's not like he had a great signature or
anything, but when he affixed it to one of his paintings, it validated
the piece, authenticated it.

So prized was Picasso's signature that it is said that when he paid
for things by personal check, the odds were that the recipient of the
check would save it rather than cash it."

Fool.co: Picasso's Checks
http://www.fool.com/news/commentary/2004/commentary04120803.htm

My Google search strategy:

Google Web Search: "bernard shaw" signature OR autograph check OR cheque
://www.google.com/search?hl=en&q=%22bernard+shaw%22+signature+OR+autograph+check+OR+cheque

I hope this is helpful! If anything is unclear or incomplete, please
request clarification; I'll be glad to offer further assistance before
you rate my answer.

Best regards,
pinkfreud

Special thanks for giving your Google strategy.

There is another one on Picasso, in a similar vein.

Someone produced a drawing and asked Picasso whether it was one of his
- he signed it and said : 'it is now'

Another interesting story I heard about GBS is that one day he enters
a bar and starts a converstion with an attractive young woman.

After some time he asks her if she would sleep with him if he were to pay her 
a Million Pounds.

To which she answers "Yes I would"

To which GBS replies "How about 50 pounds"

And the woman replies "Who do you think I am a prostitute?"

and GBS further replies "My Dear , we have already established that! I am now 
                         just is negotiating price"

DPRK007