There is a bug in the default Wordpress Import/Export Tool – for some reason it doesn’t honor the selected template and exports them all [insert frustrated angry face here].
A very convenient solution is to use the Single Post Exporter plugin (found in your Admin > Plugins)
If I want to Export a Beaver Builder Template, Row, or Module I have created and saved, it is now simply a matter of going to
Admin > Beaver Builder > Saved (rows) > and hovering over the one I want to export, then clicking ‘export’. This will download an XML file which you can then import to your site using Admin > Tools > Import > Wordpress Importer
it will now show up in your saved Beaver Builder Templates, Modules and Rows