The three conversational positions of the bag give her staff direction as to who she'd like to talk to, and for how long, but it serves one extra purpose. Inside her bag is a purse. At a formal dinner, when events are drawing on for longer than the Queen's liking, she'll reach inside the bag, grab her purse, and place it on the table.
If the purse is on the table, the Queen has had enough, and wants the event to end in five minutes time. Her private staff are responsible for keeping an eye out for these signals at all times, and five minutes gives them long enough to commence wrapping-up proceedings without appearing rude or abrupt to Her Majesty's guests. It also allows the Queen to escape from long social engagements without giving away the fact that she's grown tired of her guests.