Where did Arnold Tustin first introduce the bilinear transform?
Even though I couldn't find a decent table of contents, I took a shot on ordering a source book of papers edited by Tustin (i.e. Automatic and Manual Control), thinking he may have included something relevant.  The direct source wasn't in there, but in a paper by B. M. Brown, Application of Finite Difference Operators to Linear Systems, the following citation is given:


  The simplest of these [approximations in the form of rational
  fractions] has been derived ad hoc by $Tustin^6$.  It is the time
  series equivalent of the operator   $$ {2\over{\delta}} \space {1 - E^{-1} \over {1 + E^{-1}}} $$
  
  This can be written as
  
  $$ {2\over{\delta}} {E - 1 \over{ E + 1 }} \space = \space {1\over{\delta}} {\Delta \over { 1 + 1/2 \Delta} } \space = \space {1\over{\delta}} (\Delta - 1/2 \Delta^2 + 1/4 \Delta^3  - \space \ldots \space) $$


That looks like the bilinear transform. The actual reference is a little vague,

$$ 
^{6} \space Tustin, A. \space \space J. Inst. Elect. Engrs. \space
94 \space (1947) \space 130. 
$$

but I'm pretty sure it corresponds to A method of analysing the behaviour of linear systems in terms of time series.  That paper has a pretty detailed exposition, and Tustin doesn't seem to cite any of his other works as references, so it's reasonable to assume that's where he first introduced it. What's really interesting is the notation he used, 
$$
{2\over{\delta}} { [1,-1] \over{ [1, 1] } }.
$$