Ulaanbaatar to Bayan Olgii

Going from east to west on a route which has drastically varying weather, terrain is not going to be easy on a short time frame. I was under less than a 5days plan to visit the west side of Mongolia (Bayan olgii). Then i need to cross to china to take the return flight. If am going to take public bus from Ulaanbaatar, it’s going to take few days to reach there. With the risk of stopping at few unknown place to transfer different buses doesn’t look like a good idea to me. I really wanted to go there, the Altai Mountain.