It does, but it's a relatively slow bus (3 hours) and leaves Vientiane bus station at 15:00. So you would want to have a low number that gets you out of the consulate early and you wouldn't want to be trying to get the 18:20 flight to Chiang Mai for example. It's the cheapest way to do it if you have loads of time though. I always get a taxi because I need to get my flight at 18:20.
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I ask around the consulate picking up for people going to Udon who want to share, there are always some going either to the city or airport, share taxi to border and then on to the airport, 50-100 to the border and then 200-400B to Udon depending on how many you get.
If you have a later flight back to say Bangkok, bus is the cheapest option and I have met people who do this. But it takes a LOOOONG time for really not that much saving, IMO.