Kii Katsura to Koyasan

hi there

does anyone know if there is a bus or bus route from kii katsura to koyasan? I will be finishing up at Nachi falls in the morning on 26 April and have then planned to leave the day to get to koya but looks like the train route is still 6 hrs 30 mins with about 5 changes so wondered if there was a simpler or quicker way. I know there is a bus from Kii Tanabe but that only leaves once in the morning so not sure if there was anything from Kii Katsura.

thanks in advance!