My wife has been slowly getting into utility cycling, but she's generally a non-exerciser (like me) who hates getting sweaty. I've been very gentle in my encouragement, and it's been working. Here's what I do:

1) When I first started talking her into rides, I made them rides that she would like. Short, slow, and stopping at antique stores and coffee shops. I try to keep it fun.

2) I always went on and on in my praise afterwards, telling her how in no time she would be faster than me, etc.

3) We did rides in the morning and evening when it was cool, so she wouldn't get hot or have to sunscreen up.

4) I built her a custom bike, and made it super pretty, so she could get excited about riding. I had her tell me her wants and needs, and favorite colors.

The result is that we now regularly ride to parties and errands.