Re: How do you get over that fear?

I guess it really depends on how well you know her and her parents, your relationship with both and the ages of you and your partner.

Being a parent is stressful and time consuming, most are looking for ways to get time away from their children for a few hours, especially if they don't have a network of friends and family who regularly look after their children giving them time alone as a couple. In modern society these networks are increasingly rare so an offer to give them time alone as a couple by taking their daughter out for a few hours is often a very welcome offer.

Of course they'll want to trust you and your motives so I'd suggest framing it as an offer of help for them as a couple if you think they could use a break away from the stresses of parenthood for a few hours. Perhaps you have some tickets you were given to a Disney movie so you thought of them. Perhaps you just bring up in conversation some past experience of a friend or family member who really needed support so you helped them by baby sitting and then offer if they want a night out or some time as a couple then you'd be happy to babysit or take their daughter out for a few hours.

You'd be surprised how much they might want that time alone. A few dates to reassure them that you're responsible then work towards something more regular, perhaps a date night for them once every couple of weeks giving you your own regular date night. You can then really develop your relationship.