How do you stop a dog from nipping when their space is invaded?

I would look into getting outside help, from a behaviorist or trainer, as they know sure-fire ways to help you out. On Y!A, the ones that don't criticize you, can only offer you a few ideas... Mine is as follows.

Get a willing volunteer (someone you know, but she does not) and maybe invest in bite-buster glooves :] . When awake, test her by having your volunteer go to pet her. If she shows teeth, reprimand her in some way. A jerk to a choke chain, a spray bottle, a tap with your foot, something that shows that you do not approve the behavior. If she lets the volunteer pet her, tell her "YES" and give her a treat. Clicker training would work wonders in this situation: when she lets the stranger touch her, you'd click and treat. (Google Clicker Training, for a ton of info).

You cannot rely on her to follow the training when she just wakes up because she's not in the right state of mind. You hear of kids getting hurt all the time because they woke the dog up: just as we don't always have rational thoughts early in the morning, neither do the dogs. If that's the case, maybe make her a little sign for her bed, or a cute jacket warning to ask before petting (that way you can wake her up gently).

At work, I would give her a crate, or something to nest in if she doesn't already. No need to shut her in there or anything, just a place where she's out of the open and can crawl in and sleep. Gives her a better sense of what part of the store is hers, and what part of the store is yours, and may help make her less territorial.

EDIT: forgot to mention: give your volunteer a gift card for lunch or a nice dinner and a movie... :]

This is pretty easy to solve with management. Giver her a space where she can sleep in the store where customers can't go. Out of sight out of mind, happy dog, happy customers.

Try to prevent people from going to pet her, but get some strangers to volunteer to wake her and pet her, and if she bites her firmly and sternly say no and gently tap her on the nose. On the other hand, if she doesn't bite, reward her with a treat and give her lots of attention.

Bite inhibition and socialization. Get in touch with a professional trainer before this situation gets out of hand. Luckily you have a small dog.

thats pretty irresponsible ..keep the dog home

It would take too long to explain here how to teach her

and it would include strangers who wanted to help out

Let her sleep in a crate and don't let strangers pet her.