What a fun question! I enjoyed this one hugely.
The name of the essay is "Morale in Banking." It's a short piece,
only two pages and does indeed include a sample letter from a bank.
Benchley does not, however, reference a nightclub in it.
It definitely does, however, mention signing a check as Peter Rabbit.
"If I, in a happy-go-lucky vein, happen to sign a check "Peter Rabbit"
(as I did once, in a playful mood,) the bank ought to know that I
wasn't trying to forge Peter Rabbit's name."
"Morale in Banking," _Chips Off the Old Benchley_ by Robert Benchley.
Harper & Row (1949), pp 195-196.
According to the copyright information in the book above, the piece
originally appeared in 1933 for the New York Mirror.
Now. As to finding it, it doesn't appear to be available for free on
the web. The simplest way would be to obtain a copy of "Chips Off the
Old Benchley." If you don't wish to pay, a library would be the best
place to go. According to WorldCat, there are well over 1600
libraries that have a copy of this book.
"Chips Off the Old Benchley" is available for purchase. The 1949
book, of course, doesn't have an ISBN, but later reprintings do.
Aeonian Press reprinted the book in 1976. The ISBN for that edition
I found the following places offering it for sale:
For all of these, I did a title search for "Chips Off the Old
Mulitple copies of this book available in various conditions and from
various sellers with prices beginning at $2.95.
Has at least 175 copies in various conditions from various sellers.
Prices starting at $1.86 going all the way to $105.00
Advanced Book Exchange
They have 312 copies, again in a variety of conditions and from
Barnes & Noble
(They have it in stock) $23.95
(Would have to be special ordered) $23.95
After initial problems trying to find this on the web, I went to a
college library, found the call numbers for Benchley's books, and
physically perused the volumes they had until I came across a likely
"robert benchley" bibliography
"robert benchley" "peter rabbit"
"robert benchley" "morale in banking"
"robert benchley" banks
"morale in banking"
MLA International Bibliography, Literature Online, assorted other
literature databases, all consulted without succes.
Alibris, abebooks.com, Bookfinder, and the other book sites, I've
before with success for out-of-print materials.
I hope this answers your question.