The Omni frameworks should be copied into Bibdesk.app/Contents/Frameworks automatically in the build process, so the resulting app can run on a machine that does not have them. You can check this by `otool -L Bibdesk.app/Contents/MacOS/Bibdesk` which should reference the Omni frameworks like this:
@executable_path/../Frameworks/OmniAppKit.framework/Versions/2001A/OmniA
ppKit (compatibility version 1.0.0, current version 1.0.0)
This tip is from the cocoadev article.