This is a known ROBLOX bug.
ROBLOX are currently developing a new bubble chat to counteract this issue and bring new interactivity to the “bubble chat” system.
Feel free to read all about that here.
Until that happens, there is no designated fix to this issue that all developers can use.
As a workaround, you could make your own bubble chat system or fork the current one in correspondence with your conversation system.
Hope this helps you out somewhat.
EDIT:
As said:
This can be kinda hacky but it should be a somewhat permeable solution.