The External libraries in TBC are defined in a folder - typically at this path
C:\ProgramData\Trimble\Block Definitions\ (this is defined in the Support - Options - Project Management
The Block Libraries are DWG files in this folder - so to export Blocks that you have created in TBC requires that you export the Blocks that you have created to a DWG File. In order to do that you actually have to have a DWG with an instance of each Block physically drawn in the DWG - however when you import Blocks it will only import the Block Definitions from the DWG file and not the whole DWG file containing the instances of the blocks.
So when you create your Blocks - you create the linework that will make up the block on the appropriate layers, and then create the block definition from those. On completion you want to draw an instance of the block in the project. It is those instances of the block that you need to create in order to be able to write out a DWG that contains the Block Definitions. If you place the DWG in this Block Definitions Folder then they will become a part of the Library, that you can import into other projects.
If you have a DWG file with all the blocks already defined in it, then you can place the DWG in this folder also and it can be used as a source of the Blocks for a project. The DWG will be added to the Trimble Library allowing you to select the blocks contained within it. You can use any DWG file for this that you may have.
Alan