I was able to pop a context menu this morning with the following code. This is called from a button on a dockable window. Hope it helps someone...
Private Sub btnContext_Click(ByVal sender As Object, ByVal e As System.EventArgs) Handles btnContext.Click
Dim contextMenuID As UID = New UIDClass()
' id property of menu from Config.esriaddinx document
contextMenuID.Value = "Dharma_Inst_CustomUIElements_Context_Menu"
Dim document As ESRI.ArcGIS.Framework.IDocument = My.ArcMap.Document
Dim menu As ESRI.ArcGIS.Framework.ICommandBar = TryCast(document.CommandBars.Find(contextMenuID, False, False), ESRI.ArcGIS.Framework.ICommandBar)
' pop context menu at mouse position
menu.Popup(0, 0)
End Sub