Police have arrested a 29-year-old man in Leighton Buzzard on suspicion of carrying a firearm with intent to endanger life.
Officers were initially called to Tesco in Vimy Road at 5.30pm on Thursday to reports of a man seen with a possible handgun.
Firearms officers attended and tried to track down the man.
After speaking to people at the scene, officers tracked a man down to a property at Willow Bank Walk and made an arrest at 6.05pm.
A gun was later recovered at nearby Clipstone Brook.