Can you tell me how to do this? I used to use Mendeley before it was bought by Elsevier, and it had a useful function of exporting your entire library to a single BibTeX file automatically each time you added a new reference. I've not found a way of replicating this behaviour in Zotero (I can manually export to BibTeX, which is great, but I'm lazy and if the program can do it automatically, I'm all for it!).
It might be different in the browser, but in Zotero Standalone (which is what I use), right clicking the name of the collection in the left sidebar will give you an option to Export Collection. BibTeX will be one of the options. It works pretty well. I occasionally had issues with special characters and had to make changes every now and then for biblatex.