We calculated distance with our calculator and with the help of International map agencies and distance between Tbilisi and Sofia is 120 km.
If you go from Tbilisi to Sofia, with normal traffic conditions and non-stop driving, you reach final destination in 1,5 hours.
Depend on car conditions and fuel quality, to travel from Tbilisi to Sofia with car transport, you need 7 gallons gallons of petrol, which will cost around 10 $ with average prices.