In what direction did the ancient people travel when they crossed the land bridge

The ancient people were moving west.

The bridge that you are referring to was called the Bering land bridge which is now the Bering Strait. During the Ice age, though this area was covered in ice which made the sea levels drop and emerged the land bridge, the land bridge was covered with grasses and low shrubs which provided food for the mammoth, horses, caribou, and bison. It is believed that the ancient people followed these grazing animals from beringia (which is now SIberia)  and into America, they are believed to be the first inhabitants of America. Over time the weather got warmer and the glaciers started melting and the bridge started disappearing into what we now call the Bering strait this all happened about 11,600 years ago 

They traveled eastward from Eurasia into North America.