There is a filter 'wp_list_bookmarks'
for the complete markup. You can use it:
add_filter( 'wp_list_bookmarks', 'wpse40213_new_classes', 10, 1 );
function wpse40213_new_classes( $html )
{
return str_replace( "class="xoxo blogroll"", "class="my_bookmarks blogroll"", $html );
}