transmongolian railway to Beijing

Hey!
We've been cycling for a while now but are have quite a hard time in Mongolia. We were thinking of cycling from UB to Beijing (or at least to the Chinese border), but it is so damn cold! We, as Belgians, are not really used to the cold... Now we were thinking of taking the train to Beijing. Does anybody have any experience with taking bikes on the train? Is it easier to take them on the international transmongolian? Or take two local trains? Is the train the cheap option or are there other possibilities...?
Any tips, advice and help is more than welcome!
regards
Nina & Gerri