The most casual search of this forum will indicate this question has been asked and answered before. In fact, a stating point would be the question asked by Mightymegs and answered by macropod just 7 posts below yours!
I'm not sure if Paul (macropod) addresses the building block in that thread (you should check) but when you know what was selected in the dropdown, you can insert some "named" building block in some "named" range using something like this:
Code:
Sub InsertBBatRange(BBName As String)
Dim oTmp As Template
Dim oRng As Range
Set oTmp = NormalTemplate
Set oRng = ActiveDocument.SelectContentControlsByTitle("Conditional Text").Item(1).Range
oTmp.BuildingBlockEntries(BBName).Insert oRng, True
End Sub