Westcliff would be an easy journey from Hockley - the school bus stops at the White Hart around 8am. You do have to change at Shenfield for Chelmsford - it takes me about an hour when I do the journey to watch Essex play cricket there.
Or SHSB? Arriva routes 7 and 8 run through or from Hockley and stop next to the school, also the Stephensons route which serves WHSB now goes on to SHSB according to the timetable on the CSSE website.
For SHSB you can also travel by train (a few minutes) from Hockley to Prittlewell station, which is about 15 minutes' walk to the school - I think this would be my choice as the trains are more frequent than the buses. SHSB as a school is very good at sport / athletics and naturally everyone has to participate in games lessons, but there is no compulsion to try for teams unless you want to.