My wife went through this (sort of). She's an avid runner that got into cross-training and then mini-triathalons, but she didn't have much bike experience. She did her first tri's last season (winning a small one in her age group).
She could spin like a demon, but when it came to the road bike, she didn't have many skills (e.g., didn't understand shifting, braking, cornering, etc.). although if you are aiming at simply finishing, I'm sure you will be able to get through the course. I'm happy to say that she picked up the basics pretty quickly, though. She's getting as addicted to biking now as I am.
I think spinning helps quite a bit in your aerobic conditioning, but there is (or can be) more to it than that. I've been spinning this winter, and I think it has helped some, but it's definitely different. Doing some weights (core and legs) seems to have helped me some, too.
You might want to check out Sally Edwards book on triathalons for women.