Assuming you mean Westcliff High School for Boys (WHSB) and Southend High School for Boys (SHSB) - ? - then SHSB would probably be easier to get to by public transport, travelling by train via Shenfield to Prittlewell, as quite a lot of boys do. Looking at the timetable you would have the choice of the 06.46 or 07.06 from Ilford, arriving 07.50 / 08.08 then a +/- 15-minute walk from the station to the school.
I don't know aboout contract / private buses from your area to SHSB or WHSB. For WHSB there is the option of train to Southend Victoria (2 minutes further on from Prittlewell), then a 21 or 29 bus from in front of the station back to the school (passing SHSB on the way on the 21
), or I suppose getting out at Prittlewell and walking not quite as far as SHSB to pick up the same choice of buses at the beginning of Fairfax Drive.
Or somehow getting onto the C2C line and walking from Chalkwell station (about 20 minutes).
(Can't help thinking there must be a better way, though...