Not all 3rd party software will respond to the commands Bridge sends it when you do openWith. Off the top of my head I'm not sure if openWith ends up sending a BridgeTalk message or some flavor or operating system or message or event (or both), but if you can get the 3rd Party application to open the file using the Bridge UI's File > Open With menu item, then I'd expect scripting's openWith to work as well.
One workaround you can try is the command line. If the third-party software has a command line interface, then you can try using app.system() to issue the commands. It's possible (on both Mac and Windows), for example, to run the DNG Converter from Bridge this way, and this is how the ExportToJPEG's "Send To Flickr Uploadr-Mac.jsx" sample script runs some AppleScript that tells the Mac Flickr Uploadr to open files. I believe that the Windows Flickr Uploadr has a command line interface, so you might try something like this...
// Make a file Object using the known path to the uploadr
var command = "\"" + uploadr.fsName + "\" \"" + fileToUpload.fsName + "\"";
app.system( command );
Note that you usually have to quote paths to files for this to work all the time. Also note that app.system() will block your script until the command returns. Finally, when I've used app.system() on windows in the past, sometimes a command that seems to work just fine from the windows Console doesn't seem to do anything via app.system(). In those cases I've found that witting out the command to a temporary .bat file and then sending the path to the .bat file to app.system() does work.
I know that I've tried before to run Flickr Uploadr windows this way from Bridge, but it was months ago, and I don't recall all the details. My recollection is that it basically worked, but the user experience was a bit clunky because of the modal behavior and because a Console window appears on the screen as the commands run, and I had to quit the Uploadr manually after upload to move on. If you are a clever windows batch file scripter (I'm not) maybe you can workaround those issues.
-David