In their account of the crash, released Sunday, Transportation Authority Police said Lake was driving alone on the eastbound span of the bridge about 8:30 p.m. Friday when her car and another one were struck by a tractor-trailer.
The other vehicle, a Mazda, remained on the bridge and neither occupant was injured.
The driver of the truck, Gabor Lovasz of Canada, was not injured, police said.
No charges have been filed, but an investigation is ongoing, a spokesman for the Transportation Authority Police said.
Authorities said the crash occurred less than a quarter-mile from shore and shut down the east-bound span of the bridge for about two hours.
The car was removed from the water Saturday.
The 4.3-mile arched, dual-span Bay Bridge, which rises 186 feet above the bay at its highest point, has long terrified some motorists. Crossed by more than 25 million vehicles annually, it connects Washington's urban centers and suburbs with Ocean City and other coastal communities - and can provide a white-knuckle driving experience, even in the best of conditions.
"The Bay Bridge has everything to fear, not just height," the late psychotherapist Jerilyn Ross once told The Washington Post. "Water, traffic, claustrophobia - anyone who's prone to suffer from a phobia has a problem with the bridge. It's the feeling of being so close to death."
For years, police offered to drive cars over the bridge for phobics; more recently, entrepreneurs have done the same. In 2010, Travel + Leisure magazine named it one of "the world's scariest bridges."
But accidents in which cars go flying off the bridge into the water are extremely rare.
"It is very uncommon for this to happen," said 1st Sgt. Jonathan Green, a Maryland Transportation Authority Police spokesman.