Which OS? If on Windows you can find your Bridge collections list at (win 7 bridge cs6 example):
C:\Users\user-name\AppData\Roaming\Adobe\Bridge CS6\Collections
The files in Collections folder are .filelist - text xml format. You could copy filelists from the old system's Collections folder to the Bridge AppData Collections folder in your new system so long as all the referenced files listed in the collection filelists are in the same disks and folders on your new system.