I have been trying to think of an instance in the New Testament where we read of Our Lord being alone with just one of the disciples. I can't think of any. I do remember that Christ was alone with the woman at the well, but I can't think of any other instance.
The reason that I have been contemplating this is because it may provide a good biblical argument against the Evangelical view of an exclusive and individualistic "personal relationship with Jesus."
Why would you want to deny or refute having a personal relationship with Jesus? First, can I say, just from a debate style POV, if you do argue such a thing with an Evangelical, you're going to only confirm
their opinion of Orthodoxy as something "un-biblical/un-Christian" or whatever. (in their mind) In fact you'd give them grounds to argue, "heck even some Orthodox ADMIT they don't have a personal relationship with Jesus, and not only that, but they are AGAINST having such a relationship."
So it might not be the best way of getting your point across. Try not to prove something in the negative, but rather look to the positive, that being Scriptures showing the need for what they would term "fellowship" in the Christian walk.
Second, why would you want to disprove something each of us should actually have anyway? This adverse reaction some Orthodox have to having a "personal relationship" with Jesus I'm finding more disturbing as time goes on. Do you not pray to Christ, privately? (and if not, what makes you think you shouldn't?) And yes, I know all the stuff about "we are praying with the saints and angels", but there certainly are some Evangelicals who would say the same thing if pushed on the subject. But even for us, there is some semblance of having a unique, interpersonal relationship with God all through the Scriptures, OT and NT. The children of Israel were united with their God, and the fullness of His presence came in the midst of them when gathered together as a community. Even today Judaism is formost a communal faith, and yet there is a strong "personal" aspect to it as well. In the OT, Moses, David, Samuel, Elijah, Abraham, Isaac, Jacob, Ishmael, Noah, Ezekiel etc all spoke and "related" to God privately as well. Psalm 50 is a VERY personal Psalm, and to suggest these people and the disciples didn't have a "personal one on one" relationship with God is in my POV wrong. (I realize you don't mean it to say they didn't have a personal relationship, but I doubt an Evangelical, who doesn't understand Orthodox lingo, would appreciate the subtleties of what you're saying.
They might ask, is every single thing we do in the context of "others"? We can only talk to God if gathered together with other Christians? And our relationship is based on communal approval and gathering?
This "can" sound a little too cult like, particularly to an Evangelical ear.
As for your question, I recall quite a few times when Jesus was alone with just one person or another. For example when Peter asked Jesus "how many times do I forgive my brother" I believe it says something to the effect "Peter came to Jesus", implying a personal (with no one else present) conversation. In Matthew 16:22 it says "then peter took Him aside"...in context of telling Jesus He cannot be killed in Jerusalem. Oh yeah, Mary Magdalene finding the empty tomb and being the the first person to talk to Jesus. doesn't get more personal than that.
There are some other examples I'm sure but these are on the top of my mind.
Not to mention the numerous cases of "personal" interaction people had with Jesus, even though other people may have been present within ear shot. The woman caught in adultery story in John implies a fairly "private" conversation between Jesus and the woman. Just because other people were present to see it, doesn't make it any less "personal".
When many Evangelicals talk about a "personal relationship with Jesus Christ" they do NOT always mean Christianity is their own private religion where they neither interact or commune with any other people EVER. (or that they don't need to do so) It is true there are a good portion who DO mean such a thing, (I know because I came from that school of thought) but I would reckon they are not the majority of Evangelicals. Most will say we NEED to have Christian relationships, worship together, pray together, and encourage each other. And truthfully, while I believe we have the "correct" theolgical outlook on this subject, in PRACTICE we are VERY weak compared to Evangelicals in this area. Most Orthodox come to Liturgy and then that's it. You don't see them against until next Sunday. But Evangelicals usually are much more interpersonal outside of Sunday worship, which is ironic considering their emphasis theologically speaking.
Anyways, that's my 2 cents...it wasn't meant to cause offense only to sort of play devil's advocate of what an Evangelical might hear when we make this sort of argument. (or at least thats what I would have heard in my Evangelical days)