'bitter night' is correct and usable in written English.
You can use it to describe a night that feels cold and unpleasant. For example, "The bitter night air seeped through my clothing, making me shiver."
A bitter night some months ago, one poor family's baby froze to death.
The Rev Jesse Jackson, astounded by what he was seeing, told a crowd on a bitter night: "This is a King moment.
The whole experience of suddenly seeing his own breath in the bitter night in Foxborough, Mass., seemed a world away from the empty field in Florida.
A bitter night in Bologna resulted in England failing to qualify for the 1994 World Cup, and this would also be the game which resulted in Graham Taylor losing his job as England manager.
"They send a very strong message to the folks out in the street who are trying to make a calculated decision on a bitter night about whether to come in out of the cold.
That is why, one bitter night in the winter of 2010, about 3 a.m., I sat down at my computer to write what would become the first post of my blog the Squashed Bologna: A Slice of Life in the Sandwich Generation.
Labour politicians talked about being "stunned" and "befuddled", and of "a cold bitter morning".
It was a bitter afternoon, and they were waiting for their hay.
For the first time on what was a bitter afternoon, the sun came out, metaphorically and literally, but Arsenal could not bask in it.
On a bitter afternoon tailor-made for slippers and television, the new-found faithful were more than happy even before a touch of panto took hold.
It had been a bitter morning, so instead of walking outside, I ducked into the center's craftsy Art Room and busied myself with assembling a collage from magazine cutouts like a psych ward patient, I scoffed.
