Edit: This is just a pure CSS solution, look to the answers below if you want something more bootstraptic.
You can use a bit of css to divide the modal body in two parts, as simple as if you do a page layout of two columns.
...
<div class="modal-body>
<div class="first-column">
<!-- Your first column here -->
</div>
<div class="second-column">
<!-- Your second column here -->
</div>
</div>
...
and the CSS
.first-column {
width: 40%;
float: left;
}
.second-column {
width: 40%;
float: right;
}
There is no need of using the grid system inside the modal, and probably the result will be worse probably if you try to fit it with spans.