My final solution ...
I am working on a 'Flexible Layout', as recommended by the guide ..
http://images.autodesk.com/adsk/files/mapguide_enterprise_2010_devlopers_guide.pdf
and this seems to be based primarily on 'Fusion', so it seems that I should be using Fusion APIs.
The following is the working javascript code that I ended up with ..
var theMap = Fusion.getMapById("Map");
var theExtent = theMap.getCurrentExtents();
var lbrt = theExtent.toArray();
var bbox = "?MINX=" + lbrt[0] + "&MINY=" + lbrt[1] + "&MAXX=" + lbrt[2] + "&MAXY=" + lbrt[3];
window.open("http://maitdevgi:8081/fmeserver/services/fmedatadownload/GeologicalSurvey/GeoscienceDataDownLoad.fmw" + bbox);
By the way, the guide above has the legacy documentation in chapter 2 and the newer documentation for flexible layouts near the bottom of the document in chapter 9. This confused me. I'd rather have the order reversed.