The Navy Yard to Shaw should be a fairly hassle-free ride, and since it's kind of in the opposite direction from most commuters for part of the way (and it's a little earlier than the 8:30am rush) it won't be too crowded.
Many GA Ave buses will pick her up to take her up to Euclid Street. I don't know the #s offhand (I think it's the 70s buses), but it's a relatively short distance so I'd venture to guess almost any passing bus will get her here.
She could likely even walk the distance, but it's uphill. I bet she'll want to walk to the Shaw metro after school (5 or so blocks, downhill, past Howard's pretty campus).
I agree with you that the Navy Yard - Shaw route is better.
Has she taken the bus, metro before? I'd give her emergency cab fare just in case there's a bad delay or something. My mom used to give me emergency $ and she'd periodically be like "Let me see your emergency $20" and I knew I'd better have it ready! I'm sure she knows about giving up her seat to older or handicapped people. And I'm also sure she'll enjoy the occasional afternoon walk past Howard's campus
You know she rides for free with her DC One card, right?