How can I tell Eagle to not export a 'part' to Bill of Materials?
I haven't seen such an option and I'm not sure whether it exists, but I can think of a simple programmatic solution. Devise a prefix for the names of the parts that you don't want in the BOM, e.g. if a part was "JP1", rename it to "NAN_JP1" (where NAN stands for "Not Actually Needed", but of course you can use any prefix you like). They'll be sorted together in the BOM, so both manual filtering is easy, or you can go for a programmatic approach using tools like grep (grep -v NAN_ «your_bom_file»).

This is not what you asked for, but hope it helps :)