如何在Python中获得BOW后保持DataFrame索引

import pandas as pd
from sklearn.feature_extraction.text import CountVectorizer

data = {'text': ['This is the first document', 'This document is the second document', 'And this is the third one']}
df = pd.DataFrame(data, index=['doc1', 'doc2', 'doc3'])

vectorizer = CountVectorizer()
bow = vectorizer.fit_transform(df['text'])

bow_df = pd.DataFrame(bow.toarray(), columns=vectorizer.get_feature_names(), index=df.index)