You will need a macro to do this. The macro below inserts all the building blocks in the attached template into the current document. Depending on where you have saved your building blocks, you will probably need to modify the macro to do the same for your BB storage template. It wouldn't be difficult to modify this code to do all templates but that can get ugly if you haven't cleaned out your default Building Blocks template yet.
Code:
Sub InsertAllTemplateBBs()
Dim i As Integer, oTemplate As Template, sName As String
Dim iBB As Integer
Set oTemplate = ActiveDocument.AttachedTemplate
iBB = oTemplate.BuildingBlockEntries.Count
If iBB > 0 Then
For i = 1 To iBB
With oTemplate.BuildingBlockEntries.Item(i)
sName = .Type.Name & ">" & .Category.Name & ">" & .Name
Selection.TypeText "===================================" & vbCr & sName & vbCr
oTemplate.BuildingBlockTypes(.Type.Index).Categories(.Category.Name).BuildingBlocks(.Name).Insert _
Where:=Selection.Range, RichText:=True
Selection.TypeParagraph
End With
Next
End If
End Sub