Iframe to external website (Chatbot)

I developed an AI-based chatbot builder within my Bubble app, enabling users to create personalized chatbots. My aim is to facilitate these users in embedding their custom chatbots on their respective websites. My preference is to use embed.js for this purpose, I have so far only managed to implement this through an iframe.

My question is: when these chatbots are embedded via iframe, how do I ensure they remain universally accessible to all users. Additionally, how do I guarantee that each chatbot accesses only its creator’s specific data set from the database.