The update zip files are available for direct download, and after you have them you can apply them without an internet connection.
Here's the index:http://bionicdues.s3.amazonaws.com/BionicUpdatesList.xml
Which lists, as the most recent:http://bionicdues.s3.amazonaws.com/BIO_1103.zip
These are designed to be used by the updater included with the game (though maybe the GOG distribution doesn't have it for some reason, I dunno), so the process of applying them may take a bit of trial and error. I believe this process will work:
1) First, please back up your install, in case something breaks.
2) download all the zip files listed in the index with a version number higher than your current version.
3) starting with the lowest-version-number one, unzip the zip file into your game directory. Make sure that it's unzipped at the right level so it doesn't all get put in a subdirectory, or start spraying stuff that's meant for a subdirectory into the main one.
4) repeat for the other zip files, in order of version number
5) copy Assembly-CSharp.dll from (game directory)/DB/ to (game directory)/Bionic_Data/Managed/ (for windows, if you're using mac or linux there are alternate locations)
6) check to make sure there's nothing else in the DB folder; if there is you might have to copy it somewhere (that folder lets us put something in there once and the updater can copy it as needed for windows/mac/linux versions since they want things in different places)
Anyway, let me know if that works for you. Basically the above procedure is all the updater does