The most common and most likely answer to this crossword clue is the 11 letter word CONDITIONER
I've seen this crossword clue in The Times
C
O
N
D
I
T
I
O
N
E
R
Buddy explains!

The straight part
We know that "bathroom product" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case bathroom product = conditioner.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 CONDITIONER mean?
CONDITIONER noun- Anything that improves the condition of something
- Hair conditioner
- Fabric conditioner, fabric softener
- Someone who trains athletes or racehorses
- An agricultural machine that crimps and crushes newly cut hay to promote faster and more even drying.