I did all of this ages ago but had to go back to texstudio etc since vim doesn't seem to have very good support for bibliography. The hacks that I tried by using zotero were unwieldy. If you could get bibtex etc to work well, let us know.
BibTeX is working fine for me via biber. If you use Linux or even macOS and set it up the way I did, it should work fine for you too. Vim itself doesn't do anything other than act as a text editor. The compilation is done by a compiler included in the TeXLive package. You need to copy the correct plugins into the .vimrc file, install them and then compile. Also, bibliographies don't autocompile as you save, you have to again run a full compile for them to show up.
I did all of this ages ago but had to go back to texstudio etc since vim doesn't seem to have very good support for bibliography. The hacks that I tried by using zotero were unwieldy. If you could get bibtex etc to work well, let us know.
BibTeX is working fine for me via biber. If you use Linux or even macOS and set it up the way I did, it should work fine for you too. Vim itself doesn't do anything other than act as a text editor. The compilation is done by a compiler included in the TeXLive package. You need to copy the correct plugins into the .vimrc file, install them and then compile. Also, bibliographies don't autocompile as you save, you have to again run a full compile for them to show up.
Hope this helps! (Sorry for the late response)