To reach Jolly Buoy Island, you will have to first reach Wandoor by road. Wandoor is 30 kms from Port Blair and the best mode of transport is the government bus. Regular bus service is available from Aberdeen Bazaar bus stand at Port Blair. It is best to catch the 7.30 am bus, which reaches Wandoor Jetty by 8.30.
The route written by Pratik is very much right. but to surf jolly buoy island, you have to get permit in advance. our hotel's care taker had arranged this permit after trying for consistent two three days. in Oct. 2017 we have paid 800₹ p.p. remember this is only permit rate. after reaching wandoor, one should have to purchase ship tickets, and glass bottom ride. overall a costly deal for that day, but it is totally worth. jolly buoy island is under control of forest depends and they control the visitors per day very limited. so try two three days advance. in addition to Pratik's answer, reach early as he said because not many ferry run for this island. and it remains opened only upto 12 o'clock. after that all tourists have to vacate the island.
To reach Jolly buoy island people have to come to Wandoor beach. This is located in Mahatma Gandhi National Park. Wandoor beach is 30 Kms from Port Blair by road. This route is same for visiting Red Skin island also. Both Jolly buoy and Red skin are located at Mahatma Gandhi National park. The normal time leaving to Jolly buoy island at Wandoor beach is 9.00am. Make sure to reach Wandoor beach before 9.00am. All the ships leave at the same time and come back together.