It might also be worth noting that all regular bus travellers can make substantial savings by purchasing a weekly ticket. Unlimited travel is available on First bus services around Colchester (in an area bounded by W. Bergholt, Horkesley Heaath, Wivenhoe & Fingringhoe) for just �12.
For �1 more (i.e. �13) an Inner Zone Colchester Borough Card gives a week's unlimited travel around the same area on the services of First, Network Colchester and Hedingham Omnibuses (as well as services, run by other companies, which are supported by Essex County Council).
If your grand-daughter lives further out, a weekly ticket wouldn't really save that much. An Outer Zone Colchester Borough Card costs �20. It includes travel on all of the operators mentioned above and covers a region extending as far as Frating, Stratford St Mary & Kelvedon. It would only save your grand-daughter �1.50 per week but it would also give her free travel at weekends, to go shopping or to visit her friends:
http://www.firstgroup.com/ukbus/southeast/esse x/fares/firstweek.php
I hope that something here is of use to you.
Chris