Well we certainly won't know if you pushed too hard as we aren't aware of how hard you pushed. If it was something that she didn't want to do and you pressured into it, then yes you're an ass. What I'm guessing is though is that she seemed keen but lacked confidence(?). It's often hard to judge the difference between a lack of belief in yourself that can be overcome with encouragement and a genuine concern that one hasn't had enough training to deal with what's ahead.
That said, my gut instinct tends to be, "if you need to ask, the answer is probably yes". I'm not judging you of course, as I'm not in possession of the facts.
Has she expressed an intention to do it again? If she hasn't, I wouldn't bring it up. If it's something she really wants to do, she'll likely realise it the next time the two of you are out on your bike and hopefully mention it then. Even if she has said she'll attempt it again, let her do it at her own pace.
Is it possible to get her on a bike away from a group of learners? The only female in a group isn't a particularly comfortable situation to be in for a lot of women. If a few of them have experience it's even worse as you feel you're holding people up (or the instructor moves on before you're ready).
I learned a lot (relatively) by going round in circles in a carpark on my dad's bike before sitting my CBT (compulsory basic training). Is it possible to use someone's bike in a secluded area or even for her to get one-to-one training by the instructor?