If you install the BetterBibTeX plugin, it has a function to keep a bib file updated (e.g., with all of the items belonging to a collection).

For your current situation, I think the best approach is to export a new bib file with a different name, then add that (manually or using the command line) to the end of the existing bib file.

In case that wasn't clear from bwiernik's post: There is no way to add items to the end of an existing .bib file from Zotero, with or without add-on, though obviously export and cat (or cut&paste) isn't all that complicated.

Was BBT allows you to do is to automatically update an existing .bib files as you add items to a collection, achieving something similar and, arguably, more convenient in the long run.