The most common and most likely answer to this crossword clue is the 4 plus 6 letter word BABY SHOWER
I've seen this crossword clue in Independent
B
A
B
Y
S
H
O
W
E
R
Buddy explains!
The straight part
We know that "Does she demonstrate pet project/ stateside gift-giving bash" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case does she demonstrate pet project/ stateside gift-giving bash = baby shower.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.