There are two parts; one is ground school theory for which you will need to do either the ATPL exams (which personally I would recommend you do) or CPL exams. You would need to check with your course provider as to whether you would be exempt any of the classroom element of these exams. My guess is that you wouldn't, I'm afraid.
Then there is the flight training. To convert an ICAO CPL to JAA CPL, you need to go to a JAA flight school and have sufficient training as is required to pass the flying skills test. This may, or may not, be less than the 30 hours required for a CPL candidate who has no other licence.
I think the bridging course to which you are referring is for military personnel who want to convert to civilian licences; I don't believe it's applicable in your case.
Cheers
Whirls