There is no restriction from the Bulgaria side. It doesn't matter if you have a single or a multiple entry visa or if you have already used it or not. If you have a valid Schengen visa, you can enter Bulgaria and stay there up to three months in any six-month period.
From the website of the Bulgarian Ministry of foreign affairs
Visa-free regime for holders of Schengen visas for a stay of up to 90
days
On 25 January 2012 the Council of Ministers of the Republic of
Bulgaria adopted a decision according to which by the date of
Bulgaria’s accession to the Schengen area, our country will
unilaterally apply a visa-free system for holders of valid Schengen
visas. They will have the right to enter and reside in the Republic of
Bulgaria for a period of no more than three months in any six-month
period from the date of the first entry, without needing to have a
Bulgarian short-stay visa. The decision entered into force on
31.01.2012.