ShareLaTeX does not have the ability to link files between projects--yet. However, the online LaTeX editor Overleaf does have this ability. Since the two editors are in the process of merging together, there's a possibility that this feature might be made available in ShareLaTeX in the future.
If you're really looking to stick with ShareLaTeX, one option you might consider is using the reference managing software Mendeley. Mendeley allows you to save references and create bibliographies that can then be directly imported into ShareLaTeX and synced as you add entries. This can be done by clicking the Menu button on the left, finding the Sync submenu, and clicking Mendeley. Unfortunately, this is currently a premium feature that requires a paid subscription.
If you're willing to use the Overleaf editor, the ability to link files between projects is available for free. You can do this as follows:
- Create the central file
- Open the project you'd like to link the central file into
- Click the Project button on the upper left
- Hover over the appropriate folder button and click the downward-facing arrow next to it
- Click File from other project
- Navigate the menu to find the central file, and select it
Using this method, not only can you link central BibTeX files into all your projects, but you can also create central command .tex files with all your favorite user-defined shortcuts and link them into your documents. Changing the central file will change each of the linked files. Lastly, Overleaf allows you to import Mendeley bibliographies for free if you wanted to try that direction.