Each bot interaction occurs in the context of a conversation. Bots store all their conversations in their knowledge base.
There is a web API "get-conversations" that will let you query the bot's conversations using a "response-search" XML argument.
If you want to display a users conversation history you would need to ensure the user is connected as the same unique user each time. Currently there is no way to filter the conversations by user, so you would need to search the conversations to find ones for that user.
We are looking into enhancing this, and providing a direct-message style chat interface into bots. So maybe better to keep a local history for now.