Utopia Coaches, based at Sherburn in Elmet, North Yorkshire, provided services to rural communities between Selby, Drax, Tadcaster and York.
The company announced it was going into liquidation in a tweet on Wednesday evening, about an hour after drivers said they received the text messages.
Utopia has not responded to the BBC's request for comment.
Read more about this and other stories from across Yorkshire
Driver Carl Longfield said he left work on Wednesday with no idea the company was going to cease operating.
"I left the depot thinking everything was OK saying, 'see you tomorrow' and I got home and got a text at about 19:55 saying 'thank you very much but we are ceasing trading at 00:01'.
"We had no idea the company was in such a bad state," he said.
"The more concern for me is the passengers we have left behind in the remote communities. They relied on our services to get into work, to school, to colleges and they've been left remote."
Richard Green, another driver, said he felt completely "deflated" by the news and said he was also concerned for passengers.
"They relied on us but evidently the company couldn't be bothered about them."
The drivers met the company's liquidator earlier.
They said they were told employees would receive two weeks' pay if they had been with the company for two years or more.
North Yorkshire County Council said it was working to offer alternatives for subsidised services, including school bus services.
It added it was in discussions with other operators about whether it might be possible to restore some of the company's commercial routes.
Bus drivers say they were told by text message their company was closing and they would lose their jobs.