Yes, there is a bus that runs from Nampa, Middleton, Eagle and Boise. It only comes through once on the way to Boise and then it makes a return trip. I live in Star and I know the bus picks you up at a church. I will see if I can find the bus schedule.
As far as I am aware there is no public transportation running between Star to Boise. There is Valley Ride and Commuter Ride which you can check out to see if they are available in those areas. I would do some research on the internet about the availability of transportation.