From your Grow tab, you can only connect the bot to pages you're an administrator of. Having permissions in the Business Manager doesn't count here. You need to be an administrator of the Facebook page as stated in the Page Roles section of the page's Settings
If you are an administrator of the page, but you still can't see it in the Publishing section, then you should go into the Grow tab of your Chatfuel bot, click the "Update pages list" button
and go through the process of granting Chatfuel all the necessary permissions. Make sure all permissions are turned on so that the integration can work without any issues.
If you still have any trouble afterwards, please send a message to email@example.com with a description of the problem.