I and 2 sons ate going to Bansko 1st April but bulgaria ski do not provide boarding lessons for under 13s . My son is 11 and has borded in the US and is reasonably good - Anyone got if there are boarding groups for kids?
As far as I know not unless you organise something privately once you get there. Book your ski pass etc before you go and then arrange the tuition once you get there. I'm sure it will be easy enough to do especially as you will be right at the end of the season.
I don't have any experience of Bansko myself but someone else maybe able to help you more.