I have plenty of first-hand experience regarding Russians visiting Germany, as well as a tangentially related account of obtaining an Austrian tourist visa.
I really do not think that the likelihood of obtaining a visa is as low as Gayot Fow made it out to be. I won't state any specific rules here (though you'd be well advised to check out http://moskau.diplo.de for exact regulations).
First, the situation, as presented by OP. The girl has everything booked in advance, tickets, hotels, the lot. Her parents would do well to provide a letter confirming their sponsorship of her trip with bank statements proving their income. This, theoretically, is sufficient to get a tourist visa. This is exactly what happened when my then GF and I decided to go skiing in Austria from Moscow. We were both students at the time, but I hold a UK passport, so I was free of the hassle of applying for a Schengen visa, while my GF had to be interviewed at the Austrian embassy. This was her first travel anywhere beyond the former USSR. But, and this may play a role, the trip to Austria was a package deal and the visas tend to go somewhat smoother in this case.
But, strangely, the OP says in a comment:
[...] I'm not sponsoring her (or even formally inviting her, unless that helps somehow) and she has the funds for the trip.
I'm not surprised, really. When I relocated to Germany, nobody among the locals could explain to me how best and quickest to invite a Russian (above mentioned GF) to visit me. It turns out, a formal invitation tremendously simplifies this process. Here (German language), for example, is a form to be filled out and handed in to the local Rathaus, where for a charge of 25 euro they will print out a nice colorful document like so, called a Verpflichtungserklärung:
EDIT: I had not realized this at first, but check out the details entered in this form, I randomly found through a google image search - they're relevant. It is indeed a German inviting a Russian woman, whom she describes as "Freundin" (friend). Pulling in my discussion in the comments to Gayot Fow's answer, it is not of paramount importance that the relationship between the inviting and visiting parties is a very deep one. Friendship does not necessarily cause a verifiable paper trail, so in principle I can invite anyone I know to some extent. So long as the invitation is in good faith, everything should be fine.
I have not mentioned proof of close ties with Russia, but at least some piece of paper, proving she is a student is probably necessary (e.g. student pass). The authorities don't seem to be too strict about it, they don't need any special official form from the university, but they would like some confirmation. END EDIT.
This is essentially a declaration of your (OP's) financial commitment to the removal of the foreigner if they overstay. The OP then snail-mails this document to the visa applicant. Because Russian post is Russian post, take some sort of express mail option (don't remember the name, in the 10 euro price range) and it still will take around two weeks to reach the recipient in Russia. Things to also mail may include a photocopy of OPs German passport. Double-check on the German embassy's website.
What complicates this particular situation, is that the visitor has her own plans for travelling through Germany, so on one hand the OP would be saying "yeah, I take her in on my responsibility, she'll be staying at my place", but on the other hand, she won't be staying at his place, she's got hotels booked and all. Of course, no one expects her to stay at his flat the whole time, but why is he inviting her, when the tone of the comments seems to suggest that he isn't intending to even meet her? I don't know, how reluctant the Germans will be to issue a visa if they feel, that this invitation isn't really an invitation, but merely assistance in obtaining a visa.
The declaration of commitment puts some responsibility on the OP, of course. He has to have a sufficient income and sufficient space in his flat to offer an invitation. He'll need to provide proof of income (Lohnzettel).
All in all, this is a perfectly feasible undertaking if OP makes a formal invitation in good faith and the visa application form is filled out carefully. The details of how to fill it out are a different matter and I won't go into this, since when I invited my GF and later wife, she genuinely visited me, stayed at my place, and was financially supported by myself.