Not sure how it would be done with a preprocess hook, but an alternative would be to instead copy field.tpl.php into your theme, rename it according to the convention of field-name-[field_name], and simply add the <span>
and </span>
elements at the appropriate points in the template, like so:
<div class="<?php print $classes; ?>"<?php print $attributes; ?>>
<span class="bg-color-rd">
<?php if (!$label_hidden): ?>
<div class="field-label"<?php print $title_attributes; ?>><?php print $label ?>: </div>
<?php endif; ?>
<div class="field-items"<?php print $content_attributes; ?>>
<?php foreach ($items as $delta => $item): ?>
<div class="field-item <?php print $delta % 2 ? 'odd' : 'even'; ?>"<?php print $item_attributes[$delta]; ?>><?php print render($item); ?></div>
<?php endforeach; ?>
</div>
<span>
</div>