Just got back from Bansko. I went with my 7 year old and before I left asked First Choice whether you could hire them. They said yes and it would just be a few pounds.
However, we found that it was very difficult to hire and when we found a helmet they charged us 50 Leva for the week!! We felt ripped off.
So if you go expecting to hire a child's helmet then there are very few available and the ones that are available for an exorbitant amount.