I suggested the trees because the OP was looking for a solution while being careful not to offend her neighbor.
The Poplar trees are really super cheap and make a great screen! We bought ours (when we lived in a different house) the size of little twigs and planted them along a wall we shared with neighbors who were always in their backyard having parties. They were really nice neighbors that we liked, but felt like we couldn't get any privacy when we went in our backyard because they were always having get-togethers.
Check out this link on Lombardi Poplar Trees:
http://www.cdr3.com/lombardy/
Within a few months those trees were already higher than the wall and by the next spring, they were probably 15 feet tall. Within another year they were 25 feet tall, and so on. They grew so fast we used to tell our young DD that we sprinkled magic growing powder on them. We had an instant fence screen (the trees also blocked out the really hot afternoon sun that came from the same direction), nice shade in the hottest part of the afternoon, so the grass grew better, and the trees made our yard more green. We were amazed at how fast they grew.