No, the Bus starts at the circle outside somewhat from the old town. It would help to know where you stay, that way I could give you directions.
Basically from the old town you just walk the Promenade(3 minutes) to the Bike and Beer Bar(which is good), turn left)away from she sea) and after a block you are at the circle and the bus station is right there
Budva has two promenades, one along the beach, the second, which you take is just one block over. That is the directions I gave