Overleaf and Mendeley have integrated to allow for easy BibTeX database import.
After clicking the Add Files button, the following window will appear.
Choose From Mendeley. You can bring in references from a specific Mendeley Group or your entire library.
The first time you do this, you’ll be prompted to connect your Mendeley account with your Overleaf account. And then authorize this on the Mendeley website.
Once these details have been accepted, the pop up box will disappear and the screen will return to the LaTeX document.
Once the file has been uploaded into the project, you can use it with BibTeX in the usual way:
If you add more references to your Mendeley library or Group, you can refresh the link to pull in the new .bib content (and the file can also be refreshed via the project menu).