I was told by some people staying there last year that the receptionist sorted them some private lessons out and they got a real good deal. you cant get up the mountain without a lift pass so I would imagin kids ski school includes ones.
Only heard realy good reports ref your hotel, the down side it is about a 20 minute trip into the ski resort, and you would need a taxi to get onto bansko at night.
we were in pomporovo in january ski passes are included in the ski school so no need to buy imagine bansko the same. we had an amazing time, bansko comes highly recommended by the ski school in pomporovo so we have booked for march half term. have fun