Yes there is a free bus on Thursdays from Arinsal to Arcalis - it leaves Arinsal at 08:30 and picks up at all stops along the way, but it's just one bus so if it's full then it's not possible to get on.
Similarly there's a service on Fridays coming from Grandvalira, scheduled to be at the bus stop by Hotel Del Pui in La Massana at 09:10, but only an option if there are space.
There isn't a service bus beyond Ordino.
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