I believe there are buses which transport passengers to and from the Visitor Information Centre; as well as add on tours to the cruise which visit destinations throughout the South West of Western Australia.
Some passengers walk to and from the Port however there are no sealed paths in place, the flies can be quite friendly and there is no where to stop for relief for 2kms or so. I've often seen the passengers walking to and from the port looking a bit uncomfortable and perhaps wishing they had travelled on a bus. So I suggest checking with your cruise liner for additional tours at destinations as they may have a direct bus to the Dolphin Discovery Centre.
The Big Swamp Park is quite central to the central business district of Bunbury, there are bus stops along the way however I'm unsure of public bus time tables. Check with Bunbury City Transport which is run by Veola Pty Ltd - http://www.veoliatransportwa.com.au. The Big Swamp Wildlife Park is a great place to visit, affordable entry fees and costs to buy feed to give to the animals - birds, rabbits and kangaroos. You can feed and pat the kangaroos here. If you are travelling with children - this is a wonderful place and adjacent to the Wildlife Park is a wonderful children's playground. Opposite is the Big Swamp which has universal walking pathways around it (approx 3-4km walk) where a variety of birdlife can be seen. It has chairs dotted around the walk to sit a while and some look out points. Once again, check with the Cruise Company first to see whether they have organised a bus to stop here. I'll try and post a picture of one our visits feeding the kangaroos - if I am unable to I'll try and post a review and add a photo. Have a great holiday!
Edited: 03 February 2012, 22:39