A 40/45 minute bus journey, I think, is quite reasonable for travelling to and from school. Once the children are on the bus, that is it - no changing buses, long walks either end (this is the case for my children anyway). It certainly helps to know that, once on, they can relax and chat with friends. My two have never complained about the length of journey, they're just used to it.
Public transport is available but we use a private company which is 100% reliable. They will get the children to and from school whatever the weather and, if they break down, another bus is always sent out. They're a brilliant company and we are very lucky.
Colchester, as lovely as it is, is a very congested town and a bus journey, say from Lexden Road to somewhere near the General Hospital could take nearly as long (if not longer) than a journey outside of Colchester. It could well be that your DD's journey could be a similar length to the above even though you may be in the same town.
The ideal situation would be if you were within a 10 minute walk of your preferred school but this is not the case for many people.