Buying a Train Ticket from Ulaanbaatar to Beijing

Hello,

I am after some help purchasing a ticket from Ulaanbaatar to Beijing. I have read previous TT post on this subject before posting this.

I am doing the Trans Mongolian Route in September but wanting to leave UB early in the week rather than a Sunday or Thursday so not using the russian 024 or 004 trains.

I think I am correct in saying there is a train from UB to Jining which runs on Tuesday's but I am not entirely sure. My question is how can I buy a ticket on-line from UB to Beijing without using an agency? Do I need to use www.urtu.net for a ticket to Jining and then cits.net thereafter?

Or is is best to use an agency like selenatravel?

Thanks in advance,
Paul