Try something like:
Application.CommandBars(100).ShowPopup
The argument can be the Commandbar index or caption.
To execute a particular command on a commandbar, try something like:
Application.CommandBars(100).Controls("Paste").Execute
To print a list of all commandbars to the Immediate Window:
Sub test()
Dim cbar As Office.CommandBar
For Each cbar In CommandBars
'TRUE if right-click
Debug.Print cbar.Name; " "; cbar.Type = msoBarTypePopup
Next cbar
End Sub
EDIT: In answer to your question about the right-click menu that you get over the HOME tab, I think it's a different kind of control from CommandBar.
To get a better idea of the right-click menu names and indexes, I've modified the code above slightly. This now tries to add a control to each right-click menu. The added control's caption is the menu's name and Index. The controls are temporary - they'll be gone the next time you open Word.
Sub test()
Dim cbar As Office.CommandBar
Dim ctl As Office.CommandBarControl
For Each cbar In Application.CommandBars
With cbar
On Error Resume Next
'this will delete any customizations
.Reset
Set ctl = .Controls.Add(Type:=msoControlButton, Temporary:=True)
ctl.Caption = .Index & " - " & cbar.Name
Debug.Print "Name: "; cbar.Name; " Right-click: "; cbar.Type = msoBarTypePopup; " Error descr: "; Err.Description
On Error GoTo 0
End With
Next cbar
End Sub
It also prints out the error message, if there was one, to the immediate window.
The reason I don't think you'll have luck with the "Home" context menu is that no control is added to it. Here's a pic of a menu with the control added: