No First Eastern National buses will run on December 31 or January 1, even though special trains run by First Great Eastern -- an arm of the same firm -- will operate to Shenfield, Chelmsford and Witham for much of the time.
The taxi alternative will cost four times the normal fare from 7pm on New Year's Eve to 7am on New Year's day, with bank holiday rates at other times.
The arrangements were revealed to borough councillors at a millennium briefing last week.
Essex County Council Transport spokesman Colin Cranley said that at an informal discussion with the bus company in September, it was agreed that services on December 27 and 28, costing £12,000 would be paid for by the county.
"It would have cost council taxpayers another £10,000 to £20,000 to have council paid-for Sunday arrangements for New Year's Eve and New Year's Day, as drivers would naturally have expected a premium.
"However, Eastern National was unwilling to guarantee any drivers to work the services.
"We felt in these circumstances that it would be better not to risk having an intermittent service, and warn people in advance."
Borough councillor Maurice Hurrell said: "The situation is most surprising and very unsatisfactory. People need to travel without using their cars to go to parties, pantos, hospitals, even shops. It's a poor show."
First EN general manager Steve Smith said that the decision about New Year's Eve was taken because the majority of businesses would be shut and it was a one-off opportunity for staff to spend time with their families.
The company was not asked by Essex County Council to tender for the operation of services on New Year's Eve and has never operated on New Year's Day, he said.
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