- Issue created by @Toki
This is almost a year old now, so maybe you've found your solution, but I wanted to offer some thoughts in case you or someone else need them.
You could duplicate the admin view of the references, something like admin/content/bibcite/reference/export. Then make that duplicated view accessible to non-admins. You can use the built-in 'Bulk update' while also changing the 'Pager' settings to allow users to view 10, 50, 100, 200, or All rows. Then a user can export all records if necessary using 'Bulk update' without having to page through. I was able to do this with 1,000 rows by changing the settings to 'Allow user to display all items.'
Views Bulk Operations does allow you to create custom code for adding different options, so that could also work if you wanted to build out an 'Export reference' option.
I used Views Data Export to add an export button to the bottom of my view, but the only option that works out of the box is CSV. I tried selecting export as BibTeX, but it did not work to display the button.