Oktavi Travel is going every Wednesday and Saturday from Thessaloniki.
The tel. is 2310233964 and 2310566445, and the addresses are Fillippou 35 and Galopoulou 13 in the Xirokrini area.
While trying to visit the office of Borjomi Travel above, I found yet another travel agency practically next door with a bus departing on a different day:
NOUGZARI TOURS
Thessaloniki address: Fillippou 37
Thessaloniki hone number : 2310 239 080
Athens address: Ynonos 302 / Omonoie Square
Email: [email protected]
One way price : € 80, Return price : € 150
Departs : Thursdays at about 8am or 9am (but sometimes at a much earlier hour such as midnight to 4am!)
Arrives : Friday evening about 9pm or 10pm
OK after even more research and legwork I have reached some generalizations (any of which may be wrong so please correct me):
The ruins of the Roman Forum of Thessaloniki near several of the Georgian travel agencies which run buses to Tbilisi:
Known agencies running buses on particular days of the week
Shopfronts of a couple of the Georgian travel agencies in Thessaloniki in the area described above:
(This answer is a Community Wiki so please correct any mistakes or add any missing or new information.)
Here is a company recommended by a Georgian expat friend living in Thessaloniki as the best:
BORJOMI TRAVEL
Thessaloniki address: Fillippu 39
Phone number : 2310 243 238, Mobile : 693 25 96 441
One way price : € 80, Return price : € 150
Duration : approximately 34 hours
Departs : Sundays at 9pm
Departs from : Laggada Street near bus stop Ergatikes Katikies
Norbis Travel in Thessaloniki is one option (Lonely Planet suggests there are others)
Telephone: 2310287721
The bus does not depart from a regular Thessaloniki bus station but from Makedonikis Aminis 7.
It goes only once per week on Mondays at 7:30 am.
The price is € 120.
The trip takes 36 hours from Thessaloniki.
(I will keep the bounty open since I still think there are apparently other possibilities besides this and I would also like to include the info for Athens)
I can’t find a lot of details, but there seems to be a bus. This website states that it goes over Athens to Tbilisi once a week.
Credit:stackoverflow.com‘