
You need to get her used to being on her own gradually. Start with 5 minutes and increase by 5 minutes each time. It will be worth the effort to take it slowly, in the long run. I can vividly remember having my first puppy, leaving the flat and standing outside the door listening for a few minutes, then going back in (and yes, ignoring when you come back, you are right there), keeping at it for a few weeks until he was used to being left.
Also when you do go out make sure she has something to DO, like a big raw meaty bone to chew on or failing that a stuffed Kong. (Just toys isn't interesting enough.) She'll then be far less likely to have time to notice she's on her own. :)