Photos on social media showed thousands of the buzzing insects took over a room at Wootton Hall Park just before an live online Q&A session was about to start.
It set staff accounts buzzing with bee-related puns.
Staff said they "couldn't bee-lieve it" when they arrived and saw the swarm.
Using the hashtags #beesintheboardroom and #stingoperation, they said: "A local beekeeper has been along and has set plans (and a magic box) in motion to move the bees safely."
They joked that Chief Constable Nick Adderley was “making enquiries as to whether we could find small enough uniforms and put them to work".
One suggested they send in a "swat team" while another said police should issue the interlopers with a dispersal order.
Members of the public were all set to quiz Response Inspector Gareth Court, head of local policing Chief Superintendent Adam Ward and two constables about life in the frontline in a session set up to as part of Response Policing week.
CS Ward, said: “Response officers are the core of any police force – they are the people who turn up to emergencies day after day, hour after hour, to help those in need.
“These officers work exceptionally hard responding to 999 calls on a daily basis - they are resilient, passionate and hardworking, and it’s a privilege to lead them.”