Bug 157072 [ActionSets][Contributions] QuickMenuAction funtionality should be made public
The QuickMenuAction class should be made public and usable by IWorkbenchWindowPulldownDelegate{2}. As it is you need to roll this functionality yourself in the run method of your delegate (and it is by no means straightforward).
bundles/org.eclipse.ui.ide/src/org/eclipse/ui/internal/ide/actions/QuickMenuAction.java
a = point.x - relativeCursor.x;
            } else {
                a = relativeCursor.x - point.x;
            }
            if (point.y > relativeCursor.y) {
                b = point.y - relativeCursor.y;
            } else {
                b = relativeCursor.y - point.y;
            }
            double dist = Math.sqrt(a * a + b * b);
            if (dist < bestDist) {
                result = point;
                bestDist = dist;
            }
        }
        return result;
    }
    private int getAvarageCharWith(Control control) {
        GC gc = null;
        try {
            gc = new GC(control);
            return gc.getFontMetrics().getAverageCharWidth();
        } finally {
            if (gc != null) {
				gc.dispose();
			}
        }
    }
}