Bootstrap in HTML Web Part

I got HTML/CSS from our Designer to implement on a Sharepoint 2010 page. This page is using bootstrap.

I implemented it with HTML Web Part and also tried to split the web page layout and work directly on aspx site. But it is not working correctly in IE.

Also tried to show the page via iframe and on Chrome it is working correctly, but not with IE.

Any advices to use bootstrap on a Sharepoint 2010 subsite (at best only in a Web Part)?