Can anyone living in Surin offer any information, on the best way to travel to Mukdahan? I do not have a car, so it would have to be by bus, van or private service.

Never done it, but the train runs from Surin>Sisaket>Ubon then from there busses go to Mukdahan

The bus you want is called the "Yellow Bus" its out of Mukdahan. VIP from the Surin bus station to Mukdahan. They have an office at the Surin bus station.

Just check at the bus station for buses going to Mukdahan to fit your schedule. Their are buses that just run within the region.

Once you get to Mukdahan you can get a bus to Savannakhet that gets you across the bridge.