Buying cheap is counter-productive because if she doesn't enjoy riding, or is at a handicap trying to keep up with you, she won't be happy and the bike WILL end up collecting dust.

But I understand not wanting to spend more dough on a possible dust magnet.

So, look for a nice used bike. Something, light and enjoyable to ride, with decent gearing for your local area. If she likes riding and gets committed, you can buy what makes sense, and sell the used one for just about what you spent, so it's like a free rental.