I am currently in a long-distance relationship with a girl who could, I believe, be trained in some manner, or otherwise be willing to engage in submissive behaviour.
What causes you to believe that? Did you ask her? Did she mention something? A conversation about this is probably a good place to start.

The thing that concerns me is that entering into that sort of relationship would require an intense commitment on both our parts, her mainly socially, but mine at least partly financially.
Entering into any relationship requires intense commitment. D/s makes some things easier, and other things more difficult.

The financial commitment may essentially be implicit, but I think it does have implications for the dom/sub relationship, particularly as I would eventually have to relocate her to where I live in order to pursue such a lifestyle.
I am not sure if this is a D/s-specific issue. Relocation is a big commitment in any relationship, especially when there are going to be financial hardships. Again, I would start with a conversation.

This whole situation is further complicated by the fact that I'm relatively inexperience when it comes to such relationships myself. being dominant certainly feels natural for me, and I feel it could def. be worked into our sex life, which was mostly vanilla when we were together.
This makes me think you have had a r/l vanilla relationship with this person. Was it fulfilling? Is this a person you want to commit yourself to? Is she willing to try? If so, you can always learn together. Don't feel like you have to be some kind of insta-Dom, nor that you have to play by someone else's rules. Do what is right for the two of you.

The important thing is that I want to introduce it as something positive, because I have lately come to believe that pursuing a BD/Sm lifestyle would be satisfying for me. Any thoughts appreciated.
I think you have two seperate issues here. 1.) Can you pursue a D/s relationship with this person, and 2.) should she relocate to be with you. Both are big questions, and both should be directed towards her.

Nobody can answer those questions for you, unfortunately.... especially when we don't personally know you, or the girl. I wish it was easier... but its not.

Good luck!