Dear Gary,
The CHEVIE package is what you really need to use but this can only be
run in GAP 3. See the development version maintained by Jean Michel here
http://www.math.jussieu.fr/~jmichel/chevie/chevie.html
Alternatively this functionality is given in the new PyCox program
written by Meinolf Geck, (this is written in Python and can be imported
into Sage). The file can be downloaded on Geck's website here
http://www.abdn.ac.uk/~mth190/
A recent preprint of Geck's details some of its features
http://arxiv.org/pdf/1201.5566v1.pdf
This program is still quite new so it may not have all the functionality
you need but the Bruhat order has certainly been implemented. There is
also DuCloux's Coxeter program, written in C++, which can be found here
http://math.univ-lyon1.fr/~ducloux/coxeter/coxeter3/english/coxeter3_e.html
This will also compute the Bruhat order.
I hope some of these references help you.
-Jay
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