I agree with the above, don't worry about the return invites - the other parents are just too busy sorting their own kids out.
I used to do the following: lots of invites, sleep overs, always take a friend with you when you have family days out, or go shopping. (My DD and a friend once had the best time ever when we went to a carpet warehouse - crazy, I know).
Be very generous with car lifts - offer to pick up/take back. I even used to take a bunch of kids to a local gym club - just so she would have friends at an after school club. She didn't like going on her own. You could even offer, if you know a friend of hers would like to do it, but the mothers too busy.
take her to the local park, take balls, bikes, games - if there's other children there, there may be an opportunity to join in.
If you don't live too far from school, get a large paddling pool, even invite the mums back for a glass of wine. Failing that, perhaps take a picnic to school pick up and go to the nearest patch of grass, maybe suggest to other mothers to join in. that way she gets to play with mates for a short time after school, and you can get to know more mums.