As allready answered in the comments: no, since residence permits (D-Visa) are national visas.
As a D-Visa holder of a Schengen Country you can only travel to other Schengen Countries based on the 90/180 day rule, without having to apply for a C-Visa if needed for your original citizenship.
But Bulgaria is not a Schengen Country (only a candidate), therefore the travel conditions of your original citizenship apply.
For Blue Card holders there are exceptions when certain preconditions are fulfilled.
The result of this form Do you have a residence document from an EU country?
- Yes - I have another residence document, issued under national rules
- Non-Schengen area country (Bulgaria, Croatia, Cyprus, Ireland, Romania, United Kingdom)
- Schengen area country (Austria, Belgium, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Italy, Latvia, Liechtenstein, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Slovakia, Slovenia, Spain, Sweden, Switzerland.)
You have a residence document issued by a non-Schengen country and are travelling to a Schengen country
You will need a visa
So the permanent residence permit, that you got in the process of the Bulgarian investment citizenship, will not allow you to
- live or visit Finnland, Sweden or any other Schengen Country
on it's own.
Bulgaria Residency and Citizenship by Investment - Golden Visas
Bond investors in the Bulgarian residency programme can apply for Bulgarian citizenship after 5 years. It is possible to fast track the citizenship option by increasing the investment amount a further €511,292.
Please note however that there is no clearly defined and predictable path to citizenship through the Bulgarian “programme”. Potential applicants are advised to contact us for individual advice if they are considering this option.