No, you cannot buy tickets for the international Beijing-Ulan Bator (and onward) train at Beijing Station nor any other station or remote ticketing agent. For individual ticket purchase, you'll need to go through CITS or another agent. I'm not a CITS fan, try this one which has a reputation as being fair, honest, and reliable (though I have not personally used, only secondhand reports):
http://www.oceantravelcn.com/trainTickets.asp?classid=3
I think you are going to find prices are standardized for this and are indeed expensive. And that most agencies will have the same policies on cancellation and penalties thereof, so be committed before you lay down the funds. The international Trans-Mongolian/Trans-Siberian is very popular June thru September so book well in advance.
Prices are quoted in USD not so much for tourists (though these days most non-tourists going this distance just fly). But when dealing with tickets that normally would be denominated in three journey segments in renminbi, tugruks, and rubles, none of which are freely convertible, it's easier just to pick a universal currency and use that to quote. You can certainly pay for the ticket in RMB--they'll just use whatever USD-->RMB exchange rate is in effect at the time you transact.
There are cheaper ways to get from Beijing to Moscow using a series of local trains. Be very careful though, as this may require more time than a Russian
transit visa will give you. For taking local trains and possible additional time that could take, you'd best have a Russian
tourist visa--which is very difficult to get outside your home country.