I thought of suggesting Perama Shuttle bus service via Candidasa or Padang Bai, but their website states that for the section from Candidasa or Padang Bai to Amed, a booking will only be accepted for a minimum of 2 people. Maybe give them a call in the morning, as they may already have other bookings to Amed.
Perama's website:
:: Perama Tour & Travel - Bali ::
The service from Candidasa or Padang Bai to Amed is shown at the bottom of the page.
PS. Bargain for a better price. They're usually amenable.