Tagbilaran has an airport (TAG) with regular flights to Manila (1 hour) and Cebu (25 minutes). Cebu Pacific, Philippine Airlines, and AirAsia all serve the route. The airport is close to the city centre — about 3 km — and taxis cover it in under ten minutes.
By sea, fast ferries from Cebu City take about 2 hours and run several times daily from the Cebu South Bus Terminal pier. Several operators including Oceanjet and Weesam Express run the route. The Tagbilaran port is in the centre of town. There are also slower RoRo ferries connecting to other Visayan islands and to Manila if you have time and low ferry-travel ambitions.