Thanks to Crys Clous, there is a new plugin for Movable Type that adds an option to the Text Formatting dropdown in the entry editing page, called QuickCode. When selected, it allows you to use the BBcode tags, like [code][code], [img], [b], [i], etc. [/code]

[b][url=thedesignspace.net]This is some code[/url] [/b]

It's available for download here