Bus driver Charmaine Laurie said her training kicked in as she swerved to avoid a car on the wrong side of the road during the treacherous weather conditions in Edinburgh.
Footage of the near-miss was caught on the dashcam of a van and went viral on social media.
The back wheels of Ms Laurie's double-decker bus skidded on the snow as she tried to avoid smashing into the mini.
She said she had very little time to react to the incident.
Speaking to the BBC's Victoria Derbyshire programme, Ms Laurie said visibility had been "very poor" at the time.
"It was just as I came up over the hill," she recalled.
"I just saw through the snow the car u-turn in front of me so I didn't have much time to react.
"I just tried to brake but my back end started to slide out.
"So I had to take my foot off the brake and just try and glide through the space that was there."
Footage of the incident was filmed on a dashcam by van driver Gareth Smith in the Fairmilehead area of the city on Wednesday.
His van was on the correct side of the road but faced being hit by the bus as Ms Laurie swerved around the mini.
Ms Laurie said the gap between the vehicles was very tight, adding: "There was a van on the other side of the road so there was very little space.
"A lot of it is just instinct but we are trained to be aware of these situations... so that's why I didn't brake heavily."
Ms Laurie had been carrying about 20 passengers on the bus in the south of Edinburgh.
She said there was very little reaction from most of the passengers.
"There was one lady getting off the bus who asked how I was," she said.
"I said 'yeah I got a fright but I'm OK' and she was like 'well done'."
She did not know Mr Smith had recorded the incident and was shocked when her husband later told her that he had seen the footage on Facebook.
Ms Laurie had earlier told ITV's Good Morning Britain that he mentioned the video when he picked her up at the end of her shift.
"I said 'funnily enough something like that happened to me'," she told the breakfast TV programme.
"He said 'you're joking' and kind of dismissed it before going back to talking about the video."
"When he went in the shop I looked at the video on Facebook and when he came out I was like: 'That was me!'."
Ms Laurie said the whole incident happened very quickly.
"It looks worse on the video than it felt at the time," she said.