It looks like this is the same known issue that causes problems with templates.
everyone-group-unable-to-see-private-templates
In this case, the ai-bot options appear, but the bot simply never responds.
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Thanks for searching for prior issues! 
I think the same applies here:
You can not give anonymous users access to the chat bot, so using trust_level_0 is an effective solution for your use case. 
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