Dear Alan,
Thanks for your help. Re-reading search path section of the manual, I also solved a path mystery of my own. My .bash_profile file began with the line:
[ -f $HOME/.bashrc ] && source .bashrc
It should, of course, have been
[ -f $HOME/.bashrc ] && source $HOME/.bashrc
Which explains why the path that I had in .bashrc was not being read by textmate.
I don't know whether that .bash_profile is standard or was written by some utility or other - I don't think it can have been me since on my own machine I probably wouldn't have worried about testing whether or not .bashrc existed.
Best wishes,
Nicholas