Am I right that we need indefinite article in this sentence:
Writing a business letter.
but we don't need any article in this sentence:
Writing business letters.
(it could be a title for a post in a blog, for example).
That is correct. Plural nouns use a definite article (ie. Writing the business letters) or no article at all, just as you did.
Here is a link that explains it: https://www.grammarly.com/blog/articles-with-plural-nouns/