Depending on the context for the sentence, there are at least three possibilities.
You are very close with (A) and (B). The exact meaning for "just" is to emphasize that the action happened in the very recent past. Another example with more context would be:
- A man arrives at a party.
- One minute later, someone asks him, "Is John here?"
- The man answers, "I don't know, I just arrived."
I am feeling that it indicates something else like I have been
speaking to only one person.
This could also be correct. If the person meant this, there would probably be an emphasis on the last word:
"I have just been speaking to him." (perhaps pointing as well, for more emphasis)
But only seeing the words in print, and not hearing inflection or seeing a gesture, it's hard to be certain.
"Just" could also be a way to emphasize that the person was speaking, but took no other action. This is why more context is needed to be certain. For example,
"This man claims you made a threatening move against him."
"No, that's not true. I have just been speaking to him."