just sub-select the col of interest:
print(df[col_of_interest].to_csv(r'tweets.txt', header=None, index=None, sep=' ', mode='a'))
by doing df[col_of_interest] you only select that single column which will return a Series, if you want a dataframe use double square brackets:
print(df[[col_of_interest]].to_csv(r'tweets.txt', header=None, index=None, sep=' ', mode='a'))
You can also pass a single list item to param columns:
print(df.to_csv(r'tweets.txt', header=None, index=None, sep=' ', mode='a', columns=['col_of_interest']))
see the docs