The proposals will be put to residents for consultation, with the set of options including reducing the fortnightly black bin collection to every three or four weeks.
Recycling collections could be cut to less than once a week under the options to be presented to residents.
Hannah Winter, 51, and her partner Sharif Hussain, 59, said the proposal was a “little crazy”.
“They already shrank the size of the bins and for the average family it won’t work,” she said.
‘‘We are very good at recycling and we take it to the tip. I think if a lot of people don’t do the food bin it will be stinky.”
Grace Billingham, 35, a mother-of-two, said the plan was not practical for young families producing more rubbish, including nappies. She said that the proposed four-week plan would “increase fly-tipping”.
‘Hard to imagine’
The move comes amid a drive by cash-strapped councils to reduce the number of black bin collections to save money and drive up static recycling rate to meet Government targets.
Martha, 31, who lives in a two-person household, said that the proposed plan was “hard to imagine” and questioned where the saved money would go.
She said the proposal would “lead more to frustration. For the people who don’t care and are happy fly-tipping”.
She added: “But if there’s a study that shows that will lead people to recycle more, that would be good.”
Cllr Martin Fodor, Chair of the Bristol city council environment and sustainability policy committee, said: “The council faces a significant challenge to ensure that our city wastes less and recycles and reuses more if we are to build a cleaner, more sustainable Bristol.
“All options remain draft proposals at this stage and no decisions have been taken, and no decision will be taken on significant changes to the future of waste and recycling services in our city without consulting with residents and engaging with businesses first.”