it needs more context to translate correctly but based on the sentence, I guess " I just finished off reading a book".
부셨습니다(original form, means break something) => 뿌셨습니다(stronger tones) => 뿌쉈슴다(a shortened form)
sometimes young people say this shortened ones to emphasis the action, and you have to guess what it means as it is not used as the usual meaning, break, and could be tricky one for foreigners.
It is a slang you might think you would look cool to others but it really doesn't. ofc, my personal view.