Merhaba.

If I say Kitap aldım - with no "bir" used - does it necessarily mean that I have bought a book or can it only make for "I went shopping for books" (but perhaps I haven´t bought anything)?

"Kitap aldım"  is --->  I bought  a book or  books. 

The question is --> Ne aldın ? 

Not necessarily the person has gone just for book shopping. He may have gone for general shopping, but just bought books. 

Or, he is listing what things he bought while he was out , such as ;

Ayakkabı,cep telefonu ve kitap aldım--> I bought shoes,a mobile phone and a book [books]

There is a special characteristic for Turkish nouns, transnumeral category or numerus indefinitus. kitap okumak may mean one book or many, and if you use plural marking here it has an individualizing function.

It is a good lesson for those who against all odds believe in the compatibility of grammatical categories in different languages.