Just created a new "pastebin" bbcode. Just use the paste's url to show the code. Of course, if the code expires, it will disappear at that time.
Example:
[pastebin]B1txGZ66[/pastebin]
One issue with it is that I can either set the height to 100% and it can create very long posts, or I can set it to a fixed height. If I set it to a fixed height, any pastes that are shorter will still take up that much space with just blank space before anything else in the post. For now, I have it set to 100%.
I believe there is a way to use pastebin's syntax highlighting API on your own site, as well. I am checking into this.