Bloomingdale's gets one out to a shopper (10)
I believe the answer is:
apostrophe
'bloomingdale's' is the definition.
I can't tell whether this definition defines the answer.
'one out to a shopper' is the wordplay.
'one out' indicates an anagram.
'to'+'a'+'shopper'='toashopper'
'toashopper' with letters rearranged gives 'APOSTROPHE'.
'gets' is the link.
(Other definitions for apostrophe that I've seen before include "Single quote mark" , "detail of punctuation" , "address?" , "At which point discarded letters" , "Mark showing omission of letters" .)