Are there any buses that run to Yungaburra from Cairns please.
Bus to Atherton then get another bus or maybe a cab. Will take hours.
No. You could catch a bus to Atherton and then taxi from there. www.transnorthbus.com/cairnsatherton.asp
Another possibility, favoured by backpackers, is this tour company that goes there each day. They may have space available if you ask them: www.onthewallaby.com/tours-from-cairns/
Some accommodation places will arrange to meet you either in Cairns or Atherton. Contact where your booked into and ask.