My wife is an occasional angler. When the weather is nice she loves to get out for pannies and perch. If it gets windy, cold, etc.. she may just sit in the van and read. She is not the "big game hunter", nor is she an outdoor enthusiast, but she don't mind.
Your girlfriend, future wife, etc..., does not have to like fishing. She just has to accept that this is your passion and give you the freedom to pursue it. You, in turn, must be just as accepting as your other half. Just make sure you set aside time to d othings together.
The idea of taking the girl out to catch pannies is the ticket. Keep it simple and fun. Do not push the serious side of fishing. That is only to be shared with fellow junkies. As you are probably going to be baiting the hooks and taking the fish off for both of you, accept that she will outfish you and never let you forget it. It's part of the fun. I've gone out with the wife and daughter pannie fishing in the boat, caught hardly a thing, and spent 2 hours fileting a boatload of large gills and crappie.