I spent last weekend teaching my gf how to board.
I never took lessons and I feel like I can move down a mountain pretty well. I'm not saying lessons wouldn't teach me anything, but I think I need an instructor to school me up good going down the mountain first.
Pro relationship tip: Don't teach your significant other to ride. You're likely to both get frustrated. It puts one of you in a very dominating and commanding role. For the continued relationship it would be best to put her in a lesson until she can link turns. Then you can step in and start having fun together. Even offer to pay 1/2 the cost. Many mountains offer group women's only lessons.
If you're willing to pay for a private lesson, I think they are worth the money for the individual attention. Ask a local for a good instructor. If you don't know someone, call a local shop and ask for a good name. Or take a group lesson in the middle of the day in the middle of the week. That's usually a private lesson at group price.
Also. You've never taken a lessons. You don't want to teach her any bad habits you've picked up. For instance, I had a habit I picked up which was stopping me from carving. On the way back up the mountain the instructor told me what I was doing, demonstrated what she wanted me to do. I started carving down the run thinking, SOB! At the end of the 1.5hr lesson I was doing dynamic skidded turns.