There are two ways to get to Oslob, Cebu City
Via Cebu City
From Mactan Int'l Airport, ride a taxi to Cebu South bus terminal approximately 30-40 minutes away and costs around 230 pesos. From there, find a bus that has a Bato-Oslob sign board in it and just tell the driver or his assistant to drop you off in Oslob where the famous "Butanding" is, they know the drop off points already. Bus fare is 150 pesos. Travel time 3-4 hours.
Via Dumaguete City
From downtown Dumaguete ride a tricycle to the bus terminal and you can ride any bus in there because all buses at the terminal will pass by Sibuyan Port. From Sibuyan Port, ride a fast craft to Liloan Port (Cebu City) that costs 6o pesos. Travel time is 30-45 minutes. From Liloan Port, hire a trike for 120 pesos or less depending on your haggling skills and tell the driver to take you where you can swim with the "Butanding".