Map thanks to translink
There is a bus service to/from Caboolture R/way Station and Bribie Shopping Centre and Woorim (on the surf side of the island)
Buses leave Caboolture just after every hour (8mins or 13mins past the hour) on week days between 6am and 8pm; & 8am - 5 pm Saturday; 9am -6pm Sundays & holidays.
From Woorim to Caboolture - similar hourly service departing 6 mins past each hour.
Route 640 originates at the most easterly bus stop (Woorim) and stops at Bongaree, Bribie Shopping Centre, Sandstone Point, Ningi and Caboolture Station.
There are other services on the Island and to/from Caboolture.
Bribie Island is just over an hour from Brisbane and only has the one bridge on and off the island. When I was a kid we used to travel across to the northern tip of the island in a boat from Caloundra.
On the island you will most likely need a four wheel drive vehicle if you wish to head out of the residential/holiday apartment areas.
There were buses around but I would say that public transport would be somewhat limited to the built up areas.