Ok, I see the issue.
The issue is that you have configured your bot's access mode to 'Users', so anonymous users will not be able to connect to your bot from the iframe (only connected users). You can either set your access mode to 'Everyone', or create a guest user to connect as from your iframe.
If you go to the Embed pane it will give you the option to enter a guest user/password (but only if your bot is private right now, I will make these options show up for access restricted as well).
You can change your bot to private to generate the code, then change it back.
The code would be,
<iframe src="http://www.botlibre.com/embedded?&chat=12551&user=guest&password=0F20EC61D288676A06B37E401E02F1F4&background=fff" width="600" height="400" frameborder="0" scrolling="auto"></iframe>