The most common and most likely answer to this crossword clue is the 4 letter word GORY
G
O
R
Y
Buddy explains!
The straight part
We know that "one part of Bloody Mary" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case one part of bloody mary = gory.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does GORY mean?
GORY adjective- Covered with blood, very bloody
- Unpleasant