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I travelled on a Saturday morning and had no problem. I was the only one that got on at Sa Pobla...
It did fill up a bit more when changing at Inca, but there are also dedicated spaces on the train for bikes (either two or four at each carriage end, can't remember.) Maybe a different story on weekdays but then it's clear from timetables which trains bikes are allowed on, i.e. off-peak.
Also worth noting that it was still a bit dark when setting out from Port de Pollensa, but it was October!
How was it taking your bike on the train? You reckon they'd be cool with three people turning up?