It will totally depend on where she is, what's wrong with the car, and what kind of cover she has.
If it's a simple roadside fix, she'll be on her way.
If it needs to go to a garage, if she has basic cover, they'll tow the vehicle somewhere it can be looked at in the morning. She needs to stay with the vehicle during the recovery but she doesn't need to go with it if it's towed.
The tow time could be dependent on whether the vehicle needs to go on a flatbed or a tow rope. A flatbed could take longer to organise.
If she has onward travel in her cover, they'll do all this, plus either get her home or to a hotel overnight. They might agree to take her to a friend's house, as long as it isn't an unjustifiable distance.
If she doesn't, she'll need to arrange her own onward travel. It sounds like she doesn't, if she's asked you to pick her up.
How long this will all take is like asking how long a piece of string is. If she's in the Scottish Highlands or offshore, it'll be a long time, possibly over 24 hours. If she's in a fairly central location, and a patrol is free and nearby, and it's a simple issue with the vehicle, she might already be on her way as I'm typing this.