This will style WooCommerce's ChosenJS select boxes on the WooCommerce checkout page to match your existing Bootstrap form styles (assuming you've made any style changes in LESS) and even replaces the default background images with Bootstrap's built in Glyphicons.

chosenjs-less-for-bootstrap-and-woocommerce-checkout.less

// first some helpful mixins
.abs {
	position: absolute;
}
.rel {
	position: relative;
}
.position(@top; @right; @bottom; @left) {
	top: @top;
	right: @right;
	bottom: @bottom;
	left: @left;
}
.lh(@line-height) {
	line-height: @line-height;
}

// now the ChosenJS styles
.chosen-container {
	.woocommerce-checkout .form-row & {
		.chosen-single {
			&:extend(.form-control);
			.box-shadow(none);
			span {
				margin: 0;
			}
			div {
				.position(@padding-base-vertical; @padding-base-horizontal; @padding-base-vertical; auto);
				.size(16px; auto);
				b {
					background: transparent !important;
					&:extend(.rel);
					.glyphicon;
					.glyphicon-chevron-down;
					&:before {
						&:extend(.abs);
						.position(0; 0; auto; auto);
						.lh(@input-height-base - (@padding-base-vertical * 2));
					}
				}
			}
		}
		.chosen-drop {
			.glyphicon-search;
			&:before {
				&:extend(.abs);
				.position((@padding-base-vertical + 1); ((2 * @padding-base-horizontal) + 1); auto; auto);
				z-index: 1020;
				height: ((@input-height-base - 8) - (2 * @padding-base-vertical));
				.lh((@input-height-base - 8) - (2 * @padding-base-vertical));
				color: @text-color;
				}
		}
		&.chosen-with-drop .chosen-drop {
			.glyphicon;
			.chosen-results, .chosen-search {
				font-family: @font-family-base;
			}
		}
	}
	.chosen-results {
		margin: 0 @padding-base-horizontal (2 * @padding-base-vertical) 0;
		padding: 0 0 0 @padding-base-horizontal;
		li {
			padding: 4px @padding-base-horizontal;
			.lh(14px);
			&.highlighted {
				background: @component-active-bg;
			}
			&.no-results {
				background: @input-bg-disabled;
			}
			em {
				//change the search string appearance in results
				font-weight: 700;
			}
		}
	}
	&-single {
		.chosen-search {
			padding: 0 @padding-base-horizontal;
		}
		.chosen-drop {
			margin-top: -2px;
			border-top-radius: 0;
			border-bottom-radius: @input-border-radius;	
			.box-shadow(none);
			border: none;
		}
		.woocommerce-checout .form-row & .chosen-search, .chosen-search {
			input, input[type=text] {
				&:extend(.form-control);
				height: (@input-height-base - 8);
				.lh((@input-height-base - 8) - (2 * @padding-base-vertical));
				border: 1px solid @input-border;
				font-family: @font-family-base;
			}
		}
	}
}