Done the journey from yerevan to tblisi yesterday, shared minibus from envoy hostel yerevan to envoy tblisi, took 5 hours and cost 8000 yervan things. 650 to the pound. If your staying in the envoy theyll sort u out but its really just a publc service that youll book onto but they do the hassle of getting you onto it cause theres no real set times. Basically leaves from some random place when the drivers got enough to make his money, 3 or 4 stops on way so not bad journey, couple of beers enroute, search internet for" marshrutka". Thats what the minibuses are called. Any hotel would sort you out I reckon but if you dont mind hostels envoy is good, helped me liads here and yerevan, probably do single rooms too.