Growing up In Camiguin I got a taste of traveling all day from Mambajao to Cagayan de Oro. That was in the 1980s when the jeepney stops at every single town.
HERE IS THE FASTEST WAY TO ARRIVE IN CAMIGUIN ISLAND.
From Manila Book a flight to Cebu. From Cebu Grab an Early flight to Camiguin And it only takes 40 mins. It is super easy.
If you are flying from Manila to Cagayan de Oro City please expect this to be more complex. This trip reminds me of the movie God's must be crazy. Although the bus is now sophisticated, having wifi, please prepare yourself for another full day of travel and somewhat costly. If you don't have patience like myself, I do not suggest using this route.
From Cagayan De Oro airport you have to grab a taxi to Agora Terminal which is about 30-40 mins ride depending on traffic. From Agora unless you get lucky you can hop on a bus to Balingoan which is another hour. Once you get to Balingoan you have to buy a boat ticket to (Port of Benoni) Mahinog.
Please expect another hour as it could take longer. However, the boat ride is fun. The only time it was fun for me is when I could see my high school crush from the other side of the boat. Once you get to Benoni you need to grab a Multicab to Tangub Naasag. Then you can enjoy our welcome drinks.