I "jump" regularly. Here in Colorado it's beautiful in the summer. Your first jump should ALWAYS be "tandem" or attached to a licensed tandem diver.
My first time as I recall some 70 or more jumps ago was one of the weirdest and most exhilirating things I have ever done. There's just something about looking out the door of an aircraft at 13,000 feet and pushing yourself to "exit".
My wife, I don't think I'll ever get her to do it, but she almost alway greets me on landing.
Some things you'll want to know are - Make SURE the "rig" you are jumping with is equipped with a CYPRES unit. - Make SURE you're tandem jumpmaster has at least 100 jumps in the landing zone you are jumping at.
Also, eveyones fear is always "what if it doesn't open?!" You have 2. A main and a backup. Your backup should be packed by a licensed parachute rigger, so if worse came to worse you'd be riding on our second chute (which I've only seen personally ONCE in 5 years).
Take your GF to an authorized jump zone and watch. People love it because it's fun. You're safer statistically jumping than being in a commercial airliner. If you have questions consult
http://www.uspa.org
Happy flying!
Bling.