How to control the space allotted for a signature in letter documents?

The distance between the closing phrase and the signature is hard coded in letter.cls; in order to modify it, you have to change the \closing command: the following code doesn't really modify the distance, you should act on 6\medskipamount, changing it into a length that suits your needs.

\makeatletter
\renewcommand{\closing}[1]{\par\nobreak\vspace{\parskip}%
  \stopbreaks
  \noindent
  \ifx\@empty\fromaddress\else
  \hspace*{\longindentation}\fi
  \parbox{\indentedwidth}{\raggedright
       \ignorespaces #1\\[6\medskipamount]%
       \ifx\@empty\fromsig
           \fromname
       \else \fromsig \fi\strut}%
   \par}
\makeatother

This is the result when 2\medskipamount is used

Note that \noindent is not needed in the letter body with the letter class, which sets zero indentation.

A simple workaround is this:

\signature{\vspace{-80pt} Susan R. Bumpershoot}