Switching to a three-weekly black bin collection will save the council £1.3m a year, while a four-weekly collection would save £2.3m, the council says.
The move has been proposed to encourage more recycling of food waste.
Bristol City Council said around 50% of households do not recycle food waste, and a quarter of most black bin rubbish is food, which could be recycled.
Around £700 of food is thrown away every year per household, the council added.
Food waste is sent to an anaerobic digestion plant and converted into energy by burning the methane waste that comes from it, with the by-product being used for farm fertiliser.
The council is also facing increasing costs of treating waste, which has increased by £4m in the last five years.
