There's a bus station, EmmaPlien, on Back Street, about a 10 minute walk from the cruise port.
Any one at teh shops along the way can point it out to you. All the buses (which are small green vans) stop there. The Mullet Bay to Phillipsburg route is a popular one. Buses have their destinations listed on a sign in the front window. Cost should be around US$ 3 per person each way. Just tell the driver where you want to go.