The Bishop of Winchester School is actually going great guns with improving and recently put on an amazing performance of the Wizard of Oz which was easily as good as if not better than the 'better' schools in the area. They have a great performing arts department so don't let it put you off OP. Worth going to see it in the flesh as it were. And for Jewell. Good luck.
Not sure where you live in Bournemouth but if near Jewell the probably near st Peter's too? If your kid went to Jewell they might end up at bishop of Winchester which doesn't have the best rep and St Peter's (Primary and secondary) has always had a good reputation. Have you considered that school?