The Chinese capital, which staged the summer Games as recently as 2008, faces an uphill struggle because the International Olympic Committee (IOC) is thought to be reluctant to award three Games in a row to Asian cities.
The next Winter Olympics will be in Pyeongchang in South Korea and Tokyo won the right to host the 2020 summer Games.
"We are making sure we are fully prepared ourselves and I hope the IOC will chose the most suitable city," Yang Shu'an, vice-president of the Chinese Olympic Committee, told a news conference in Sochi when asked about the issue.
The IOC will make its decision on the venue next year.
Russia has spent $50 billion (30 billion pounds) on the Games and related developments around the Black Sea resort of Sochi and the IOC is concerned about such spiralling costs for Olympic hosts.
Stockholm pulled out of the race for 2022 last month, the Swedes saying the financial sums did not add up. That left Beijing to compete with Norwegian capital Oslo, the Polish city of Krakow, Lviv in Ukraine and Kazakhstan's Almaty.
The Beijing bid is a joint one with the city of Zhangjiakou, in Hebei province, some 220 km northwest of the Chinese capital and an area which officials say has a long history as a ski centre.
The iconic "Bird's Nest" stadium, the centrepiece of the 2008 Games, would host the opening ceremony, while Alpine skiing and some sliding events would be held in the mountains midway between Beijing and Zhangjiakou.
Work would begin this year on a high speed railway line that would cut the journey time between the two main cities to just an hour and should be completed by 2017.
"In 2008, Beijing delivered a truly exceptional Games. We hope to fulfil the dream of a summer and winter Olympics in the same city," said Yang Xiaochao, deputy mayor of Beijing.
He said the rail link would be completed whether or not China got the Games. The bid is designed to promote winter sports in China, the world's most populous country and home to an expanding middle class.
"Winter sports in China are not very well developed. It would help to boost winter sports in China," said the deputy mayor. He would not be drawn on how lavish a Games China would stage, saying only that spending would be kept within an unspecified budget.
Sports politics observers believe China could be doing the groundwork for a future bid. It got the summer Games only after suffering the disappointment of losing out to Sydney for the 2000 event.
(Writing by Keith Weir; additional reporting by Karolos Grohmann, editing by Ed Osmond)
