Josie James, from Clwt y Bont near Caernarfon, had been discharged from a mental health unit despite having "murderous thoughts towards herself".
An inquest heard her parents had not been given clear advice or an emergency phone number.
A narrative conclusion was recorded.
Miss James died in August 2015. The inquest heard on the day of her death she had told a friend she was going to jump off the bridge.
The alarm was raised immediately but she had already gone over the side.
Pathologist Dr Mark Lord said she died from a ruptured major artery due to a fall from a height and said she would have died on impact.
Miss James' mother, Joy James said: "As a family we have no interest in pointing the finger at any individual. We just want lessons to be learned."
In a statement, Betsi Cadwaladr University Health Board said: "We acknowledge that there was no effective communication with her family.
"We are working hard to improve the way we work with families, which includes ensuring they are supplied with treatment plans and additional information and advice to support the ongoing care of our service users."
It added families of patients can access its intensive community treatment team, and they are asked how they wish to be communicated with when patients are admitted.
A user group has also been set up, which the health board said helps it "listen and learn about how to make significant, meaningful improvements" in the care it provides.
Recording a narrative conclusion, assistant coroner Nicola Jones explained that she was going to move away from a suicide conclusion because it was not clear what Miss James' state of mind was at the time.

Police said it happened near a garden centre at Rogers Farm on the A24 near Findon, West Sussex.
The 79-year-old victim died at the scene, at about 20:40 BST on Thursday. A murder investigation is under way.
The suspect, described as a tall, skinny, white man in his 30s, is thought to have been driving the car in front of the man who was stabbed.
The attacker is said to have shoulder-length, wavy brown hair and was thought to be driving a pale "old-style" car.
It is believed the victim was travelling alone and that he was stabbed more than once.
Det Ch Insp Karen Mizzi said: "Officers have been urgently making inquiries overnight to trace the suspect.
"We need to hear from witnesses who saw the collision, the suspect or the car involved, particularly if anyone filmed the incident or saw anyone filming it."
Laura Muchmore, 21, who works in the garden centre close to the scene of the stabbing, said: "It's especially shocking that the victim was an old man.
"Findon is a really lovely little village. It's so picturesque and it's not known for this type of crime."
Edmund King, president of the AA, described it as a "horrific and tragic incident".
He said: "Thankfully, such brutal 'road rage' attacks are generally a rare occurrence on our highways.
"It appears that some drivers do react differently when they are behind the wheel than they would if they were walking down the street.
"They almost feel that the car empowers them but in reality it does not."

It will bring together British, Irish and German naval representatives, along with 200 descendants of those killed.
The event is being held on the centenary of the Battle of Jutland, the biggest and deadliest sea battle of the war, when 6,000 men in the Royal Navy were killed - 358 were Irish.
The commemoration will take place on HMS Caroline.
It is the only remaining ship from the 1916 battle off the coast of Denmark.
The battle was fought between 31 May and 1 June 1916 and involved about 250 ships.
It saw the Royal Navy's Grand Fleet, based at Scapa Flow in Orkney, clash with the German High Seas Fleet.
The centenary of the battle will be marked in Scotland, where a service in Orkney will be attended by German President Joachim Gauck along with the Princess Royal.
Representatives of all the nations connected to the battle, including Ireland, will attend that service.
A service of remembrance will also take place on board HMS Duncan at Jutland Bank, the site of the battle.
There will be a live stream of the ceremony on the BBC News NI website from 12:20 BST on Tuesday.
A health board has acknowledged there was "no effective communication" with the family of a 15-year-old girl who fell to her death from the Menai suspension bridge.
[NEXT_CONCEPT]
A manhunt is under way for a driver who stabbed another motorist to death after a collision between their two cars.
[NEXT_CONCEPT]
Belfast is to host a special all-island commemoration for Irish sailors who died in World War One.