So here is the update for you.
The bus to Kibber goes from Kaza at 4:00 PM and after dropping the passengers at Kibber it reaches back at kaza in the same evening.
There are probably two buses from Kaza to Reckong Peo one in morning and one in afternoon, and this part of the road is pakka road. They go via Dhanker but reportedly from a trekking distance of about 2 kilometers, and a road distance of about 8 kilometers. If you can trek that much, that won't be a problem. Yet I am not sure it can be that the bus goes via this small alternative route that runs through Dhanker itself, in that case you can step out of the bus next the gate of the monastery.