course i looked for it and i didnt found it : here are some Info's about the Route from UB to Beijing
First Option: Direct-train. Problem: expensive (ca 60$)
Second: nigth train from UlaanBaator to Zamyn Uud (Bed ca 10$), in Zamyn Uud on 7-8.00 in the morning, one of the plenty minibusses outside the trainstation to Erlian (first town chinese side) for about 50yuan (takes a couple hours) and then (one of - when i was there, there where 5) the sleeperbus from Erlian to Beijing, departure around 2.00, in Beijing the next morning (120yuan).
That makes together around 28-29$ - half the price.