We've been working away on integrating Twitter Bootstrap with ExtJS 4 and have just released the work completed so far on GitHub!
You can find the project details here. http://bootstrap.newbridgegreen.com
It is still a work in progress but it was a common request on here and in our inbox, so we thought we'd get it out there to get feedback from the community.
We will be working on the documentation on how to use all the components if there is demand, but currently about 80% of the bootstrap classes exist in the theme to help with laying out your application, so you can use the standard docs to help.
You can also use the customise page on the bootstrap site to generate a file to edit this theme.
Anyway. Have a look, let me know what you guys think.