What if your brand new shiny Russian girlfriend comes over on an airline from Russia. Obviously you can fly her around the UK, but can you fly her GA all around Europe?
Somehow I don't think so, but I don't even know where one might start looking.
You can't even
drive her around Europe without an appropriate VISA (tourist or otherwise). Once she gets a Shengen VISA she can move freely around the Shengen area, for countries outside the Shengen area local rules apply which may be completely different going from one country to another.
The embassy of the country you plan on taking her to might be a good place to ask for authoritative info.
Ciao,
DG800