An inmate hanged himself two days into his sentence after telling jail staff he found it hard to ignore voices in his head telling him to end his life, a report said.
Michael Berry, 24, was the eighth inmate to take his own life at HMP Bedford since 2017.
The Prisons ombudsman said "significant issues remain" in the delivery of [the mental health] service" at the jail.
A Prison Service spokesman said all the report's recommendations were accepted.
Mr Berry, who had a history of substance and alcohol abuse and mental health problems, was remanded at the jail on 8 March 2017, after appearing in court charged with 22 offences, including kidnap and sexual assault of an adult male.
The report said court staff emailed the prison's mental health team requesting an assessment of Mr Berry's risk to himself, but the jail's team had no record of this correspondence.
He was then assessed at the prison's reception without documentation, and self-harm and suicide procedures began.
The following day there was a care review but the report said "healthcare staff were not invited, despite Mr Berry saying that he heard voices telling him to kill himself".
The ombudsman said this "should have prompted an urgent mental health assessment and a referral to a GP to consider prescribing antipsychotic medication as a matter of urgency".
Instead they increased his observations that day and the next, but on 10 March he was found hanging in his cell, and died in hospital on 16 March.
A Prison Service spokesman said: "This is a tragic case and our thoughts remain with Mr Berry's family and friends.
"We accepted all the recommendations from the Prisons and Probation Ombudsman and the prison has since made a number of improvements to the work it does to prevent suicide and self-harm."
There have been no deaths at the prison in 2018.