Gilimanuk is the port for public ferry’s to Banyuwangi on Java. The ferry’s leave day and night, there is no time-schedule. It takes about 1,5 – 2 hours.
Tickets can be bought at the port.
At bus-station Ubung in Denpasar you can buy a bus-ticket to Banyuwangi on Java (or other cities), the ferry is included in the ticket.
In Banyuwangi is a train-station. You can go by train to Surabaya or Yogyakarta. There are several good hotels in Banyuwangi.