If you look at Twitter's own container-app.html demo on GitHub, you'll get some ideas on using borders with their grid.
For example, here's the extracted part of the building blocks to their 940-pixel wide 16-column grid system:
.row {
zoom: 1;
margin-left: -20px;
}
.row > [class*="span"] {
display: inline;
float: left;
margin-left: 20px;
}
.span4 {
width: 220px;
}
To allow for borders on specific elements, they added embedded CSS to the page that reduces matching classes by enough amount to account for the border(s).
For example, to allow for the left border on the sidebar, they added this CSS in the <head> after the the main <link href="../bootstrap.css" rel="stylesheet">.
.content .span4 {
margin-left: 0;
padding-left: 19px;
border-left: 1px solid #eee;
}
You'll see they've reduced padding-left by 1px to allow for the addition of the new left border. Since this rule appears later in the source order, it overrides any previous or external declarations.
I'd argue this isn't exactly the most robust or elegant approach, but it illustrates the most basic example.