Actually 160 USD isn't too far off from the government price. The international tickets are only sold through travel agencies and the government forces the price on them.
That said there are a variety of option but most will take you more time.
Option 1.
Probably the most common. Take the overnight bus from Beijing to Erlian, arrive in Erlian, arrange to pay for a ride across the border and catch the train on the other side. There is a daily slow train and several times a week the faster express train (this is the same train that crosses the border).
Option 2.
Buy a ticket to Erlian. There are only a few trains per week direct from Beijing.
#3 departs Beijing on Wednesdays for Moscow
#23 departs Beijing currently on Tuesdays and Saturdays but at somepoint (perhaps already passed) it will only operate once a week and which day is never clear.
#4652/4653 departs Hohhot for Ulan Bator twice a week, on Mondays and Fridays. You take the train from Beijing to Jining South and then connect with this train to Erlian.
Get off in Erlian, cross the border and continue.
Option 3
A few intrepid travelers have reported buying a ticket from Beijing to Erlian and then buying a supplement from Erlian to UB on board. I wouldn't recommend this in summer or on the #3 train to Moscow, but on the #23 or the connecting from Hohhot, this might be worth considering.
Costs will depend upon whether you are traveling hard sleeper, soft sleeper or seat (only to the border). Even upper and lower berths have different prices. Tickets for domestic travel can be purchased at the train station.
http://www.travelchinaguide.com/china-trains/ will give your their prices for tickets. Buying them at the train station is cheaper.
The ride from Erlian to the Mongolian side costs about 80-100 yuan.
I don't have current information about fares from Dzamin ude to Ulan Bator but be aware that the earlier you get to the Mongolian side the better chance you have of getting a ticket same day to UB and Dzamin ude is reportedly a pretty miserable place with little to offer.
This post from summer 2007 by manulike with update from Nov 2008 has useful information: Erlian Fact Sheet.
Ruth