This trip will take 2-2,5 hours, including stops to have a rest, take a photo etc. When you'll be back to the starting point you can grab a beer or lemonade at one of the restaurants there. Feeling hungry? Order some fish in Gaztelugatxe or walk back to Bakio. If you feel like travelling somewhere else you can take a bus from Gaztelugatxe to Bermeo - it's a nice fishermen village where you can have some fresh fish. Unfortunatelly we didn't made it to that village, after the lunch we came back to Bilbao.
Trip advice: if you decided to visit this place in any season but summer. When you'll just arrive to Bakio you will see a lot of taxis waiting right next to the bus stop. Taxi driver will take you and other people who will fit in his car to Gaztelugatxe for just 1,30€. If you will take this taxi some other time, it will cost you 10€! Same system if you want to go from Gaztelugatxe to Bermeo - you need to wait when the taxi from Bakio will arrive and if there will be some room for you 1,30€ and you're travelling with comfort.
In summertime you just need to wait for another bus which will cost the same price as bus-taxi - 1,30€.
Enjoy your trip to wonderful Gaztelugatxe!