Councillor Holland "fundamentally disagreed" with the amendments
The Labour leader of Bristol City Council said she and her cabinet resigned after the majority of the chamber had lost confidence in them.
Cllr Helen Holland stepped down after the budget meeting following an amendment over plans for a household waste incinerator at Avonmouth.
This was supported by Ms Holland's Labour group but opposed by the Liberal Democrats and the Conservatives.
Liberal Democrat leader Cllr Barbara Janke has taken charge of the council.
It is the seventh administration in as many years for Bristol City Council.
Councillor Holland said as a minority administration it would not accept amendments which exposed council tax payers to "huge additional costs".
"Taking forward a policy we did not believe in would have no credibility with the people of Bristol.
"It was clear the majority of the council chamber had lost confidence in us so the right thing was to walk away," she added.
Conservative leader Richard Eddy said his party's patience has run out.
"It should not come as any surprise, we opposed the administration last May.
Cllr Janke says there are a number of outstanding issues
"Two weeks ago there was a vote of no confidence on policy issues.
"This was a de facto vote of confidence in the budget process."
Ms Janke who has taken over as council leader said she had expected the electorate to decide who runs the city later this year.
"This is a great privilege. There are a number of outstanding issues that need to be tackled urgently.
"We are pleased that the budget has been set, and will be seeking to put a Liberal Democrat administration into effect as soon as possible and set some clear priorities.
"It's not a particularly easy time at the moment with the recession and job losses.
"There is clearly a lot to be done," she added.