The airport was evacuated for more than six hours, after the “package” was discovered on a Ryanair flight from Alicante, according to reports.
The airport was reopened when police later gave the all-clear, but flights on Sunday continued to be disrupted.
It transpired that the threat was a written hoax bomb threat.
A spokesperson for Ryanair said: “This flight from Alicante to Bristol (22 Aug) landed normally at Bristol Airport last night.
“During a routine inspection, a written hoax bomb threat was discovered on the aircraft.
“Police carried out a security search and cleared the aircraft to return to service… Ryanair sincerely apologised for any inconvenience caused.”