I couldn't find a way to export *all* citations from **My Library** (it seems to only work one page at a time), but it's possible to save all citations from the edit mode of **My Citations**:

 - Log in to https://scholoar.google.ca
 - Click [![enter image description here][1]][1]My Citations
 - Click the leftmost checkbox on the bar at the top of the list of citations:
[![enter image description here][2]][2]
 - Click **Export > BibTeX** and choose **Export all my articles** then **Export**
[![enter image description here][3]][3]

You should get a browser window with the BibTeX file of your citations that you can "Save as..." or copy/paste to a text editor and save.

  [1]: https://i.sstatic.net/0tUZT.png
  [2]: https://i.sstatic.net/nIwUK.png
  [3]: https://i.sstatic.net/tYroR.png