I was thinking, for Ten and my OC, they would first meet as my OC is helping her catering company with a wedding (or some other special event), and my OC finds out that an alien is impersonating the bride in order to be able to influence the groom into allowing the alien race into somehow controlling the human race later on in history. Of course, the tenth doctor would be there to get at the alien and bring the real bride back.

I'm open to suggestions if you want to change this idea a bit. 
If you don't like this idea at all, I would be happy to go with an episode where the tenth doctor first meets an assistant for the first time (I can't remember which it was though DX)