Text Classifier with multiple bag-of-words
I cannot comprehend the question completely but let me see if I got this right. 

You want to train a classifier. You have different columns for subject and body. You have now pre-processed it in a manner such that subject and other meta information have been removed. 

Now I shall try to answer your question. Keep in mind that, this is how I would approach the problem (based on experience with similar task in the past) but there could be better ways or approaches. 

I would not remove the subject column in the first place. I would also not train the classifier on two separate bag-of-words. I would append both, the subject and the content, into one single document and then classify them accordingly with one unit of bag-of-words instead of two. 

Why would I do this? There could be times when the subject could have keywords or something that could lead to better classification than the body of the email. The vice versa could also be true. Hence, without having seen the entire dataset, and to be on the safer side, I would also give this approach a shot. Compare both of your approaches and then see where you have better scores of accuracy, precision, recall and other metrics that aids you in your conclusions. 

Ways to accomplish this? Yes, NLTK is one way to get the bag of words. However, I would go ahead with scikit-learn package to train my classifier. I would also run LSA/LDA/HDP (Topic Modeling Algorithms) to see what constitutes my data. To do this, I would use Gensim. 

http://scikit-learn.org/stable/

https://radimrehurek.com/gensim/

Additional tutorials to help you get started with text classification if you are new to it (that is what it seems like, pardon me if I am wrong). These will also help you in achieving better results to begin with:

https://towardsdatascience.com/machine-learning-nlp-text-classification-using-scikit-learn-python-and-nltk-c52b92a7c73a

http://zacstewart.com/2015/04/28/document-classification-with-scikit-learn.html

Although both the tutorials I mentioned primarily concentrate on binary classification, you can also achieve fine-grained (multi-class) classification in similar manner.