£200 to have your windows cleaned is a lot. But if you live in a 10 bed mansion then whatever you have done is going to cost a lot. Imagine the quote if she decided to have new curtains all round!
Not really for us to say if you're too expensive or too cheap, but from experience, stick by your price. She probably hasn't got a clue what she should pay to have her windows cleaned, thats why she thinks it's a lot.
Probably when she puts her Merc in for a service and they charge her £400 she'd be shocked, but the garage won't negotiate, will they, she knows that and glumly pays up.
Wealthy people are usually no happier parting with their cash than the rest of us, in fact their often mean with it.
Get the job, do it, you'll soon know if you've charged right at the end, you can't lose it's only window cleaning, but you can learn from it. You'll probably wish you'd gone in a bit higher. She'd be shocked whatever.