Most visitors arrive Sibu by plane, if you travel directly from oveseas. If you are coming from other city in Sarawak, then you will have the choice of buses.
There is direct flight from KL or JB to Sibu. Malaysian Airlines and Air Asia are the one that you look for. MASWings serves flights between cities and rural areas in East Malaysia, including Sarawak and Sabah.
Travel to Sibu Town
Bus 3A runs to and from town every 1½ hours from 6.30am to 6pm (RM2.50, about 30 minutes). You could also try flagging down any rural bus that passes by. The coupon taxi fare into town is RM28.
The local bus station is on the waterfront. To get to the long-distance bus station, take Lanang Road bus 21 (90 sen) from the local bus station. It leaves roughly hourly between 6.30am and 5.30pm. A taxi costs RM10.
**Resource from LonelyPlanet
Sarawak has land borders with Brunei, Indonesia and the Malaysian state of Sabah. If you have own transport, you may drive all the way to Sibu
This is the most common transport if you are travelling between cities in Sarawak. The travelling times can be long because of the distance.
Express boats run from the coast inland along Borneo's larger rivers. They are generally faster than buses and cheaper than planes. Popular routes include Kuching-Sibu (4 hours) and Sibu-Kapit (3 hours). You may read more on Sarawak Transport on Lonely Planet website. http://www.lonelyplanet.com/malaysia/malaysian-borneo-sarawak/sibu/transport/getting-there-away