The main way that people travel to Hatobuilico by public transport is either to catch a bus from Dili to the turnoff of to Hatobuilico, which is about 40 minutes beyond the town of Maubisse, then walk or catch a lift with a passing truck or car from the corner to Hatobuilico. (approx. 1.25 hours by vehicle or 4-5 hours to walk).
You can also get a lift on an anguna (the Timorese version of the truck turned into people carrier) or a truck carrying people or goods to Hatobuilico. You can ask to sit in the front of the truck with the driver, or you can sit or stand in the back with the local people. Expect to pay $4 or $5.