"I’d been driving home late that night."
What hides under "I'd"? If it is "I had", then it seems Past Perfect Continuous tense suits best here, but Past Perfect Continuous supposed to have two actions, isn't it? So, I'm confused, please help me with clarification
The shortened word is indeed "had". "Would" is also abbreviated this way, but makes no sense here.
The past perfect continuous tense refers to something that continued (in this case driving) before something else in the past. Nothing else is specifically mentioned, so the later time is the time that the sentence is set.
Because narratives are usually in past tense, and there is no specific later time mentioned in the sentence, your sentence sounds much like a sentence from a narrative, as I implied in my comment.
It's "had", as you suspect, and this is indeed the past perfect continuous (or "past perfect progressive") tense. I'm not sure what you mean by "two actions". There are already two verbs here: "been" (past participle of "be") and "driving" (present participle of "drive"). It doesn't require another one.
