I married a non-cyclist. Over the years she gave birth to two cyclists and became one herself. So I pat myself on the back for expanding the cycling community by 3. hahaha
In all seriousness, the first step is not too push too hard. My wife first started riding out of necessity. As a non-citizen upon arrival in the U.S. she wasn't able to get a driver's license right away. I built up a comfortable mountain bike with an upright position and a woman-specific saddle, added some fenders and a rear rack, and got her comfortable with running errands in the area. I never expected her to get more serious than that.
Over time she decided she wanted a road bike. I built her a "plush" bike... Klein Aura V setup with a triple. Eventually she was riding longer distances and made the switch to clipless pedals. We started riding together more and more often but not at my pace... we rode at hers. It certainly wasn't conducive to my fitness, but the time together was great. Usually, I hauled our Burley trailer with my son in it so I got a workout, but not the same kind of workout I would get on a solo training ride. Often, I would go out for a couple hours on my own before embarking on a shorter ride together. Once my oldest son was big enough to ride his own bike, these turned into family outings.
My wife is now a hardcore cyclist. She's not a racer. But she rides nearly every day. She rides with the boys to school. She runs errands by bike. She does the shopping with a bike and trailer. She rides the local trails for recreation and fitness. On Twitter she is @bicyclemum and she even started a blog under the same name... sharing our adventures on (and off) the bike. She has a slick, carbon fiber, di2 road bike and a sweet carbon, full-suspension mtn bike. She loves her bikes and loves to ride.
The bottom line is to help your partner remain enthusiastic. Make sure she is comfortable and enjoying herself. I felt it was worth the investment to give my wife quality bikes with a good fit even before I was certain she would get into the sport. Nothing curbs enthusiasm quicker for a newbie than being in pain during a ride. Next was to encourage her without pushing. I know I am not the most patient person so I had to be extremely conscious of my attitude when riding with her and not allow myself to get frustrated with her pace or her apprehensions... just shifting gears or changing hand positions can be really intimidating for a beginner.
If the opportunity exists near you, get your partner into some ladies-only rides. My wife LOVES riding with other women. The more experienced ladies can always offer advice and there tends to be a bit more "chick-cred" about saddles, shorts, creams, and other products coming from other women than from us guys.
Bottom line (as you mention in the heading) is to be patient. You have years of cycling experience (I assume) so it will take a while before your partner can even keep up with you. But, if you're in it for the long haul, it is worth the time and energy to develop her skills so you can enjoy cycling as a couple.
One more benefit... once you convert her "cyclist" she will never say no to a new bike, bike-related product, or bike trip ever again. Well, almost never.
The beginning... non-cycling, soon-to-be-mum.
Now... @bicyclemum
She does however appreciate Rule 9 as we tend to be applying that one at lot at the moment. 
