There are no regular bus services from Amed to anywhere else in Bali. If you really want to get a local bus you need to get yourself to Culik on the main island ring road and flag down a passing bus from there. The vast majority of travellers however use either the Perama service, a shuttle bus (essentially a shared minivan) or hire a private car and driver. The shuttle buses are generally the best deal, but they rely on a minimum number of passengers so if there are not enough passengers you need to pay for the extras, nego or it is cancelled.
Perama shuttle bus
This bus operates from the Perama office in Amed, so you'll need to get yourself there first. It's a good idea to book your ticket at least a day beforehand in order to know you have a seat and to be sure the bus is actually running. Sample destinations from Amed:
Airport: Departs 11:00 175,000 rupiah
Candi Dasa: Departs 08:45 100,000 rupiah
Kuta: Departs 11:00 175,000 rupiah
Padang Bai: Departs 08:45 100,000 rupiah
Ubud: Departs 11:00 175,000 rupiah
Other shuttle buses
These "shuttle buses" are sometimes minivans and sometimes private cars. It varies. Likewise the prices vary for no clear reason. The following were signboarded at a few travel agencies and work on a minimum number of passengers (generally two to four). Shop around for a rate and departure time that works for you. Prices are per person, not per vehicle.
Airport: 150,000 - 225,000 rupiah
Candi Dasa: 125,000 rupiah
Gilimanuk: 400,000 rupiah
Jimbaran: 170,000 - 250,000 rupiah
Kuta: 150,000 - 225,000 rupiah
Legian: 150,000 rupiah
Lovina: 180,000 - 200,000 rupiah
Munduk: 300,000 rupiah
Nusa Dua: 160,000 - 300,000 rupiah
Padang Bai: 130,000 - 150,000 rupiah
Pemuteran: 350,000 rupiah
Sanur: 140,000 - 200,000 rupiah
Seminyak: 150,000 - 225,000 rupiah
Tirta Gangga: 100,000 - 120,000 rupiah
Ubud: 140,000 - 200,000 rupiah
Hiring a private car and driver
If you can't find enough passengers for a destination you want or you need an unusual departure time, you'll need to hire a car and driver. Bank on at least double the prices listed in the "Other shuttle buses" section above, and be prepared to shop around for a reasonable rate. Also ask at your accommodation for a rate to use as a baseline -- whatever they charge you should be able to get it for less outside by yourself. Expect rates to jump over public holidays and again, plan ahead as with lead time your driver may try to get extra passengers to spread the cost.
Amed offers the quickest way to get from Bali to the Gili Islands off the northwest coast of Lombok. Services generally go daily (weather permitting) with a couple of departures a day running in high season. All speedboats leave from and arrive at Jemeluk bay.
A word of warning: as with the operators out of Padang Bai, this is cowboy country so do not expect your speedboat to follow safety (or any other) standards that you would expect in more developed countries.
Online reviews of speedboat services to the Gilis are near uniformly scathing. Boats are routinely overloaded, breakdown, run late, are randomly cancelled and so on. A number of speedboats out of Padang Bai have caught on fire (a friend received third degree burns in one such fire) and they do sink on occasion. The operators are reckless. Simple as that.
A regular complaint is operators not dropping at Gili Meno, despite promises otherwise. Yes, at around 40 minutes, this is the quickest way to the Gilis, but personally we would not use these services and if you have the time, we recommend using the slow boat service from Padang Bai.
If you decide to use them, a one way ticket should cost between 250,000 and 400,000 rupiah. It is a good idea to book a day in advance to be sure they're not "full". Rates on operator websites bear little relation to reality. For instance according to Pacha's website, a one-way fare from Amed to Gili Trawangan in July should cost 800,000 rupiah. We were quoted half that from travel agents in Amed.
Kuda Hitam: Departs 09:00 http://kudahitamexpress.com/
Pacha Express: Departs 09:00 http://www.pacha-express.com/
Sea Express: Departs: 09:30 http://www.gili-sea-express.com/
Amed is spread out over a series of sprawling bays and is therefore difficult to get around without your own transport. This becomes especially apparent if staying in accommodation that is away from restaurants or the best snorkelling spots.
It's a good idea then to either rent a motorbike, hire a car or stay in a location with greater access to restaurants and good snorkelling. The most central areas are from Amed through to Bunutan.