The most common and most likely answer to this crossword clue is the 7 letter word HAIRDOS
I've seen this crossword clue in The Guardian
H
A
I
R
D
O
S
More clues leading to the result HAIRDOS
Buddy explains!

The straight part
We know that "Bob dreads pageboy" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case bob dreads pageboy = hairdos.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 HAIRDOS mean?
HAIRDOS noun- A hairstyle.
- A haircut.