One thing Bulgaria does not have in great abundance is… islands.
In fact, there are but a handful of isles, sometime just rocks, off the Bulgarian Black Sea coast, and none of them is permanently inhabited except for the usual lighthouse keeper. However, one of them, near Burgas, has recently been refurbished as a growing tourist attraction.
The island, now serviced by regular commercial boats, was used as a monastery, a prison, again a prison and for about a decade after the fall of Communism was all but abandoned. Not any more. Spending a day and a night there may not be a particularly unique experience for someone from Greece, Scotland or Croatia, but it does hold the promise of offering the sort of solitude in such a short supply along the Bulgarian Black Sea coast.
Where in Bulgaria are you?