The byelaws, which would apply at 212 sites around the city, are intended to replace outdated Victorian rules.
Among the full list of byelaws, one in particular has campaign groups worried. It states that "No person shall without reasonable excuse remove from or displace within the ground...any stone, soil or turf or the whole or any part of any plant, shrub or tree."
Friends groups and foragers fear the rules would make it a crime to pick wild blackberries, mushrooms, or even make daisy chains.
Another bylaw explicitly prohibits camping, which has led to accusations of discrimination against homeless people.
The council explains in its consultation documents that "the byelaws will enable the council and partners to tackle nuisance and other anti-social behaviour that can hamper the enjoyment and safe use of the city's green spaces. The 24 new byelaws focus on ensuring everyone can continue to use Bristol's parks responsibly, considerately and safely."
Anyone who breaks a bylaw would be removed from the ground and would be subject to a fine of up to £500.
Bristol Council's spokesperson told local news website Bristol 24/7 that it was trying to allow as much activity as possible while also controlling anti-social behaviour. The spokesperson said everyone's views would be taken into account as part of the consultation process.