Hi roma ... from what I can see, the airport is approximately 13kms from Brive.

According to the airport website, there are 4 car rental companies:
http://www.aeroport-brive-vallee-dordogne.com/en/practical-information/taxi-car-rentals.html

No mention of an airport bus service on the website, just taxis. Unless anyone on the forums has any further info, it might be worth trying out some of the contact details on this page:
http://www.aeroport-brive-vallee-dordogne.com/en/contact/phone-email.html

David

Perhaps your hotel might be able to arrange a transfer to meet your flight or suggest a bus route. I too couldn't find anything to help.