The circumstances would have to be that the bullet missed. It’s not really any more complicated than that. You put a round in the general vicinity of someone, and didn’t quite connect, but you still tore up some tissue on the way through.
This can just be the result of poor aim, situations where a character is just pointing a gun rather than actually aiming it. Though, someone who doesn’t know what they’re doing and is trying to aim could also result in a glancing blow. Or, if both the shooter and the victim are moving, then hitting a target accurately is a lot harder, and a glancing blow like that is certainly possible. I don’t want to say, “more likely,” because it’s not really a common outcome.
There’s a slightly rarer situation where a shot directed at the head will skate across the skull, it’s one of those “the world is a weird place sometimes” kind of fluke things, but it does happen, rarely.
Range only makes a glancing shot less likely, but it also reduces the chances of getting hit, so, not really a concern.
In general, she probably wouldn’t lose consciousness. At least not from blood loss. Having a panic attack because someone just shot her
in across the head isn’t out of the question.
Honestly, I’m not certain about how much blood. Glancing wounds will result in a disproportionate amount of blood for the severity of the wound, but it shouldn’t be life threatening. So, someplace between, “more than you want to see,” and, “not enough to kill you.”
It’s also worth pointing out that this kind of injury is rare enough that my writer’s guide to forensics has nothing on the subject, so I’m kind of flying blind here.
This probably would result in a long, shallow gash and not much else, which means it would need to be treated like any minor open wound. That is to say: disinfect (with peroxide, or alcohol), staunch the bleeding with gauze (ideally with antiseptic ointment added to the bandages, once treatment gets that far), and if the bleeding persists, get someone to sew your character up.
If this happens to you? Go to the ER. This is about as non-lethal as gunshot wounds get, but that doesn’t mean you should mess around with it, also douse whatever you cram in there with either alcohol or peroxide first, you do not want to mess with an infection if you don’t have to, and impromptu bandages are as good a vector as anything.
If the bullet takes off her ear, or part of it, that would probably require reconstructive surgery. Even if it doesn’t, she’ll probably end up with a nasty scar as a result.
Sorry, the wound info is a little more speculative than I’d like, but I don’t have anything solid on hand, so I’m having to do it mostly off the top of my head… so to speak.