Robert Boyd-Stevenson, 38, of Headford Road, Bristol, had admitted a charge of making a bomb hoax by communicating false information last year.
He texted security threats to a phone linked to the airport on 29 August.
The airport remained open but raised its security threat level and police officers were called to the scene.
Days earlier, Bristol Airport had been evacuated in a separate, unconnected bomb scare.
CCTV footage showed Boyd-Stevenson topping up the phone in Knowle West at 05:39 that morning and in the airport itself at about 06:00 BST.
He was sentenced at Bristol Crown Court on Thursday.
PC Simon Broad said the "strength of evidence against him" had meant Boyd-Stevenson admitted his guilt early on.
"Robert Boyd-Stevenson intended to cause disruption to staff and passengers at Bristol Airport, as well as the emergency services, through his reckless actions," the officer said.
A spokesman for the airport said the sentence would send "a strong message" about making bomb threats.
He added: "Only the prompt and professional action of Bristol Airport staff and Avon and Somerset Police on the day prevented significant disruption to the travel plans of thousands of passengers."
A man who made bomb threats to Bristol Airport in a series of text messages has been jailed for two-and-a-half years.