I think there are a couple of public bus options from rayleigh. First no. 25 and arriva no. 1. No. 1 will mean a walk from the London road, which plenty do. An octopus four weekly ticket costs £44 and can be used on both arriva and first buses.
I thought that I only paid £42 for DS2's current Octopus, but it may have been £44! The Stephensons bus is useful if you are on its route and if an Octopus card can be used, which I assume it can. As it is only a limited service, if your DD wants to take part in an after school activity or hang out in Leigh or Southend for a while with friends, being able to just go on a 'normal' bus would be a bonus.
Other options are the 20 to Bridgwater Drive (c. 10 minute walk to school via Treecot Drive), the 3 to Chalkwell schools (10-15 minutes via Nelson Road and Eastwood Boulevard or Nelson Rd / Manchester Drive / Middlesex Avenue) or the X30 to Kent Elms (add on crossing the A127 and a walk halfway up Bridgwater Drive to the no20 option). It depends on whereabouts in Rayleigh you are starting from?
Scary Mum - this is actually not a very long journey - e.g. from the nearer parts of Rayleigh, the no 20 or the 25 take about 20 / 25 minutes to get to DS2's school, which is a bit further than the school the OP is asking about. Rest assured we are not in Southall to Hampstead Garden Suburb territory here