Until the 12 month is over you are allowed to drive using your foreign licence. You won't need to put on 'L' plates or similar as well. However if you want to keep on driving without restrictions you have to pass the driving test before the 12 months are over.
From the ask the police site:
While your full licence is valid, you can drive any type of small ...
Your non-UK license remains valid, and is not voided by the issuance of a UK provisional license.
You can drive a small vehicle (motorcycle or car) in the UK for up to 12 months using your non-exchangeable non-UK license. See the presentation on this UK govt webpage.
Whether you can hire a car in the UK using your non-UK license will depend upon the class of ...
Is an “International Driving Permit” from the AAA in United States valid in Bulgaria?
Yes. Here is the list of countries in international driving permits issued on 2019-10-14 by AAA in United States. It includes Bulgaria: