SHSG is direct train from Romford to Southend Victoria then bus from the interchange just outside the station - either a no 27 which stops about 5 minutes' walk from the school, or a no1, which stops opposite the school but goes down to the travel centre and almost all the way back up before turning off into Southchurch Road. Or (and lots of girls do this) a short walk to pick up the 1 (or a 4 / ?4a) at a different stop, on its way back from the travel centre.
For WHSG by train it is either Romford - Southend Vic then no 21 or 29 bus via Victoria Avenue (both runs outside the Westcliff schools), or change to c2c at Upminster for Chalkwell (c.20 min walk to WHSG, nice long hill passing our road on the way up from the station but loads do it
), or Southend Central (buses as before, but from the travel centre so another 5 minutes on the journey. Getting out at Chalkwell, you are okay on the train arriving at 0802, but you probably need an earlier one to go via Southend Central.
Of course, there may be private minibuses etc to WHSG. DD - year 9 at SHSG - has friends who come from as far away as Barking on the train but I've never heard her mention anyone travelling by minibus.