Hi Selkie. If you’re heading across the Bonaparte by going south to Pt Keats, then west to Berkeley, you will get Telstra 3G near Port Keats, then perhaps a little Telstra 3G reception from Wyndham about 2/3 way across the BG on a good night. From there on, you might as well turn your phone off.
McGowan Island Camping Ground have satellite internet at the house, which you can connect to via their wifi for a small fee.
Mt Gibson Iron on Koolan Island run an Optus 3G network on the island, but I took an Optus modem stick about 3 years ago to try it, and couldn’t get enough reception to get on the net.
Silver Gull Creek (Shelley and Mal) have satellite internet, but I’m not sure if they will let people use it.
All the best, Ross