the bus i took was horrible 5 years ago, maybe there are other options now, the bus was packed with very loud tourists ( i wont mention where they came from... )
budget thailand has no oneway charge if u rent more 5 or more days...
In Chiang Rai the car can be very useful as well :]
Over the years I've probably taken Green Bus 4 or 5 times (CNX-CEI/Nan/Lampang) and was always one of the only foreigners on the bus.
Perhaps it's more of a 'luck of the draw' scenario.
I'd much prefer renting a car and driving, and subsequently getting outside of town as well, but for o/w trips that's not necessarily practical.