He may feel like he does not get the attention he deserves from you when other people are around and will do anything just to gain it thus turning to a bully. You can try talking to him about his behavior calmly and explain why he cannot get it as much when other people are around.
Oh the power war is on. Ok some ideas Prepare him for what will happen if he behaves or miss-behaves. Empower him to make the choice to decide reward or consequences for the next time you are talking with an adult. Teach him to hold your hand if he wants to ask you something when you are with another adult. Maybe give him a notepad to write on so he can write you a note. Let him know he Is very important to you and sometimes he has to wait his turn for you to be available. Let him know you Deserve respect and expect him to respect you. Set up a special time for the two of you to be alone together without interruptions. Like a date and time for him to be excited about. Be strong and make your boundaries very clear. It's a process for him to learn and might take a while but he will get it. Be sure to say nice things about him to others so he can hear you Its fun and will raise his self esteem and reassures him that he is important to you. Good luck!