Why would Bronn follow through with Cersei's orders?
She gives him a wagon-load of gold and sends him off to kill her brothers, who both happen to be good friends of his and are hundreds of miles away from her sphere of influence. She also is known for treachery and likely won't pay him the rest upon completion.
You really think he won't either join them or just take off with his gold?
No way is Bronn going to try to kill them. What would be in it for him?