Rent contract and consent letter

The contract is simple rental agreement between yourself and the owner of the property. It have to be notarized. You'll have to give someone a power of attorney also notarized on order for him to represent you at the notary, otherwise the notary can't verify the signatures of yourself abd the owner.
The written notice is kind of declaration from the owner that he/she gives their consent for you to live in their place. Thi also have to be notarized. These ywo documents you'll have to provide to the consulate with the Visa D application.

Emanuela, thank you so much for your help.  I have been very confused by this part of the process.
So do I make a written statement giving a friend in Bulgaria power of attorney for me and have it notarized here?  Do I need to mail the statement to him in Bulgaria or can I email him a copy of the notarized statement to present to the Bulgarian notary?   Thank you again for your help.

You have to give to your friend a notarized power of attorney in order for him to represent you in front of Bulgarian notary and to sign on your behalf the rental agreement.
The owner if the property have to sign a written consent in front of the notary that he agrees with you living in hus place.
Both of these documents have to be sent to you so that you present them in the embassy for your visa D application.