Getting from Ulan Bataar to Beijing

My wife and I are going to be in Mongolia for a few days. We are looking at leaving on a Monday and get to Beijing sometime Tuesday. Though I see the Trans Siberian
comes by only Sundays and Thursdays. Sunday is too soon and Thursday is way too late.
So with the exception of flying out. Is there another way of getting there. Perhaps by a combination of domestic train and bus?

For domestic train schedules within Mongolia and for international train schedules out of Mongolia, take a look at the web of Urtu.