Is your current plan to live in Dupont indefinitely?
These bus suggestions are good ones, and a bus can be a great option for most mornings. But I can tell you from experience that if you want to have a degree of meaningful engagement with your DC's private school experience, once you have done it for a while it is going to get really tiring and tough for you to live relatively far away, and you are going to spend a lot of time in the car. There are going to be mornings where one of you wants/needs to be at school for a while before heading to work, and then you're talking about a lot of time in the car and leaving really early in the morning, unless DC is at someplace like Maret or Aidan (in which case you don't need a bus anyway).
This is not to say that I'm suggesting you move to the burbs, as compared to perhaps neighborhoods further NW in DC where there is a bit less drive time. You may still end up using a bus at that point, for example with Potomac which has bus routes throughout the District.