Timid about a B&B that's dirty? (6)
I believe the answer is:
shabby
'dirty?' is the definition.
(thesaurus)
'timid about a bb' is the wordplay.
'timid' becomes 'shy' ('shy' can be similar in meaning to 'timid').
'about' indicates putting letters inside.
'a'+'bb'='abb'
'shy' enclosing 'abb' is 'SHABBY'.
'that's' acts as a link.
(Other definitions for shabby that I've seen before include "Down at heel" , "in worn and dirty clothes" , "needing renovation" , "'Scruffy, tattered (6)'" , "Badly worn" .)