CityFlyer Express is one of BA's franchise partners. Although they do have business class I wouldn't spend any miles to upgrade your friend as the cabin layout for business and economy is the same; 2-2. They fly mainly ATR-42 and ATR72. The only two benefits of business class are a little bit better food (but it's only a 90 min flight) and lounge access. You better save your miles for next time and upgrade her to Club World or First
I don't know how many miles you need to upgrade, if you can upgrade at all. For European EC members this is not possible. I don't know about UK/US members.