要对双向链表按字母顺序进行排序，可以使用常见的排序算法，例如冒泡排序、选择排序、插入排序或快速排序。下面是一个使用冒泡排序的示例代码：

class Node:
    def __init__(self, data):
        self.data = data
        self.prev = None
        self.next = None
        
def bubbleSort(head):
    if head is None or head.next is None:
        return head
    
    # 计算链表的长度
    length = 0
    current = head
    while current:
        length += 1
        current = current.next
    
    # 冒泡排序
    for i in range(length-1):
        current = head
        for j in range(length-i-1):
            if current.data > current.next.data:
                # 交换节点的数据
                current.data, current.next.data = current.next.data, current.data
            current = current.next
    
    return head

# 创建一个双向链表
head = Node('d')
node2 = Node('b')
node3 = Node('c')
node4 = Node('a')

head.next = node2
node2.prev = head
node2.next = node3
node3.prev = node2
node3.next = node4
node4.prev = node3

# 对链表进行排序
sorted_head = bubbleSort(head)

# 打印排序后的链表
current = sorted_head
while current:
    print(current.data)
    current = current.next

输出结果为：a b c d