The journey to Bako has two stages; the first stage can be made overland but the park itself is reached only by boat.
A bus ride from Kuching to Bako Market takes about 45-60 minutes red public bus number 1, originating from the wet market and costs RM3.50 each way. Buses leave to/from Bako about once every hour starting from about 7AM from Kuching and finishing about 6PM from Bako, but the schedule is not firm. You can get a daily schedule at the bus station 1 in Kuching next to the open market, near the main mosque in the morning.
The other travel option is by minivan, which departs from the same location as the bus throughout the day. Minivans depart when full, or when the waiting passengers offer the driver enough money. A minivan can be chartered for around RM30, and seats 5-7 people. They can reach Bako in half the time of the public bus.
Hotels and tour operators also offer regular shuttle buses; as a pricier but more reliable alternative.