Could you please explain what you mean about boys bullying him?
I don't think RGS is sporty. All independent schools offer sport, and RGS is pretty much baseline, you really only get more sporty than them. The more academic schools like RGS will tend to do less sport, whereas the less academic ones, like Reeds will have more sporty types, and hence do more sport.
The 11+ system is in fact quite common among 13+ schools, they do more of an IQ test at 11, and then follow up with the Common Entrance at 13+ to do the full spectrum of subjects, but essentially if you passed at 11+ for a given school you are 95%+ likely to pass the Common Entrance for that school. And in any case you can apply at 12+ for RGS.
If your son is beyond Y6 at Y5, then he should be looking at one of the top selective schools, there are some lists here:
rankings.ft.com/secondary-schools/secondary-schools-2012
RGS is the top choice in your area, at #15 on that list.
Hampton #21.
City of London Freemen's School #45 (don't know much about this)
Brighton College has buses from areas south of Guildford
www.brightoncollege.org.uk/media/20160/bus_routes.pdf
Reigate Grammar.
Another list here:
www.telegraph.co.uk/education/leaguetables/9551003/GCSE-results-2012-Independent-school-results-table.html
There are more choices a bit further out of reach, e.g., St Albans, Haberdashers Askes, Merchant Taylors, Sevenoaks, Caterham, Whitgift, etc.