Twitter Bootstrap sideways caret

Just switch up the borders (see fiddle):

HTML

<b class="caret-right"></b>

CSS

.caret-right {
    border-bottom: 4px solid transparent;
    border-top: 4px solid transparent;
    border-left: 4px solid;
    display: inline-block;
    height: 0;
    opacity: 0.3;
    vertical-align: top;
    width: 0;
}