Silly shower base without shower (14)

I believe the answer is:

scatterbrained

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'silly shower base without shower' is the definition.
I can't judge whether this defines the answer.

'silly shower base without shower' is the wordplay.
'silly shower' becomes 'scatter' (I can't explain this - if you can you should believe this answer much more).
'base' becomes 'bed' (both can mean the bottom of something).
'without' indicates putting letters inside ('without' can be similar in meaning to 'outside').
'shower' becomes 'rain' (synonyms).
'bed' enclosing 'rain' is 'brained'.
'scatter'+'brained'='SCATTERBRAINED'

Can you help me to learn more?

(Other definitions for scatterbrained that I've seen before include "Empty-headed" , "easily distracted - with 20d" , "not together" , "Disorganised and unable to concentrate" , "Unfocused" .)

I've seen this clue in The Times and The Sunday Times.

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