Matthew Wain, who covered his face with a hood as he entered court on Wednesday, made a YouTube video of his threats towards the Birmingham hospital.
Wain, aged 31, of Hatfield Road, Birmingham, pleaded guilty at the city's magistrates' court to sending a grossly offensive or menacing message by means of a public electronic communications network, relating to the video.
Prosecutor Peter Lawn told the court Wain posted the "lengthy" video on YouTube, describing how he had previously attended hospital "having a heart attack".
During threats made on the video, which police said featured a phone call to the hospital, Mr Lawn said: "He is unhappy with treatment he received.
"He also states 'not being funny, but what happened to me yesterday, I will bomb the place to be honest.'
"He also states that he hopes all the staff die of coronavirus."
Mr Lawn added: "It is the threat to bomb the hospital that brings the defendant before the court today."
Magistrates heard Wain was arrested on April 1 and told officers he "didn't mean it" and had no intention of harming anyone.
He also stated that he had made "empty threats" on the video, and had been upset and hurt at his treatment.
Wain, who has previous convictions, including a malicious communication offence committed in the Norfolk area, was granted conditional bail pending pre-sentence reports.
He was ordered to return to court on June 18 and instructed not to contact NHS staff unless it was for a genuine medical need.
The Sandwell and West Birmingham NHS Trust, which runs City Hospital, has seen more than 360 deaths of coronavirus patients since the start of the pandemic.