Congrats on the new gf. Regarding bike touring with her: start with getting her comfortable on some short day rides. Borrow or rent an appropriate sized bike for her, make certain it is fitted properly. Skip the fancy cycling shoes, they will only complicate things for a newbie! But, pay attention (and $$) on a good saddle. I've been through this process with my wife and her sore butt really cramped her enthusiasm for cycling in any form. Good padded shorts and a female specific saddle made all the difference. Once you're riding let her set the pace and distance, prepare to ride short, slow rides initially. Bring snacks to share when you take breaks and take breaks often. If she enjoys the first couple of rides, she'll want to continue and she'll develop strength and stamina pretty quickly. Once she's riding regularly (like weekly or more) then look at buying a good bike, not before. As for touring, in time that will develop on its own. Do not rush this process!
I've been down this path with my current wife and I have learned what worked and what didn't. She'll never be as passionate about cycling and touring as I am, but after several years of preparation, we did spend three months cycling across France last year, so there is one data point of success.
Good luck, have fun!
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