My wife and I were there recently, arrived at Mukdahan on Monday, stayed at a local hotel.
Up early Tuesday morning and drove to friendship bridge. Parked at parking area near border and paid over 200 baht for overnight parking. Went to border crossing office for foreigners, filled out a form and paid a fee. Got a bus ticket and proceeded to Savannakhet Thai Consulate. On Laos side various kinds of transport is available and we went to restaurant opposite the consulate and waited till 9. o’clock for office to open. Soon as people lined up we joined them and handed in relevant paperwork and received a voucher to return next day.
Got a hotel close by, stayed the night and returned Wednesday about 1.pm to line up between 2-4. Presented voucher and everything returned with the yearly Non o based on marriage.
Headed back to border crossing completed TM 6, got stamped and hopped back on bus.
Next day reported to local immigration as had to be done within 24 hours. Appears that tuk tuk and taxis generally charge 100 baht per person for transport to Thai Consulate.
Hope this assists as what we did was mostly based on advice from Tod Daniels.
Be aware that if it’s a wet day protective clothing and plastic folders will help as you will find yourself waiting in an outdoors area.