UB to Bayan - by train - any suggestions?

I will be in Mongolia in late May and need to catch a train from UB to Bayan.

Has anyone done this trip or have any suggestions?

First, I think there is more than one Bayan in Mongolia.

Second, I think there is VERY little train service in Mongolia apart from the route from the Russian border to the Chinese border.

Third, I know of no information about Mongolian train schedules on the internet apart from some limited information here: limited Mongolian Train schedule.

Ruth