I hitched a ride one year with friends, but it's really hard to find anybody who wants to go, who will drive me. I've never heard that they had a bus.
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"If we won all the time, we'd be as unpopular as Ferrari, and we want to avoid that. We enjoy being a team that everybody likes." Flavio Briatore
I don't know if there is a special bus from the circuit to the town but there is a regular bus. If you walk the road passing the main entrance northwards (is it D139?) you'll find bus #6 and it seems to go pretty often. It's a ten minute walk from the main entrance to the bus stop.
For travelling back to the circuit at friday night,
there are a lot of locals who try to earn a bit of extra money by being a taxidriver for the night.
Last year we went with 5 people in one car plus driver for about half the price of a real taxi