If I were you, I wouldn’t let your friend dictate the terms of the conversation with regards to this question. Because what she’s ultimately asking is, “Why don’t you Catholics believe in the Bible alone?”
Turn the tables on her and say/ask, “Do you want to know why Catholics believe that, or do you want to talk about why sola scriptura is in error?”
If she really wants to know why Catholics believe that, then remember these points and use them.
There are ultimately, very few Scriptures that can be used to support the Catholic belief, explicitly, but there aren’t any that deny it either. This is because the Catholic position is NOT universalism, which says that no matter what, everyone is “saved”. This is a common misconception of critics.
The Catholic position is, that if one has no possibility of encountering the Gospel message in this life, then they are only bound to the natural law inscribed in every heart. Besides, IMO, when your friend asks you the question she did, it’s apparent that she hasn’t thought of this question: “Well, if ‘belief in Jesus’ is an absolute requirement for entering the Kingdom, then what about babies that die before they have a chance to ‘choose’? Oh, there’s an ‘age of accountability’? Show me the ‘age of accountability’ in the Bible.”
The point is that your friend is making the common mistake of linking “belief” and “grace” inexorably. They are not inexorably bound however, and indeed this is the only, rational way we can claim God is “just”. God, being sovereign, can and does pick and choose whoever He wants. This “picking and choosing” is normally done through the Sacraments, where grace is infused in the recipient, however, while we are bound to the Sacraments, God is not bound to the Sacraments, and thus, can “save” anyone.
So, returning to the verse your friend likes, let’s examine it with the view above: John 14:6 Jesus saith unto him, I am the way, the truth, and the life: no man cometh unto the Father, but by me.
This is saying exactly what Catholics believe, that is, on occasion, God chooses to pour out the grace of His son even on those who have ever heard His Gospel. This however doesn’t mean that they “believe” in Him; this doesn’t even mean they are “guaranteed to be saved”, as that would violate the doctrine of free will. They simply profit from the grace of our Lord Jesus Christ just like anyone else who has been Baptized in the normal fashion. Put another way, the people have the grace sufficient, even though it isn’t readily apparent.
The most critical point to remember with your friend here is that no where in John 14:6 does the word “believe” appear. Thus, in that verse, God is not limited by man’s belief, AND THUS, that verse cannot be used to support a “Christians only” mentality.
The natural reply to the point above is, “Well how do you know then you are saved? If it’s just God choosing, how do you know?” Easy, by being a Catholic and receiving the Sacraments, the means by which God has revealed He WILL and DOES dispense His Grace, this is how anyone can know for certain they are on the PATH to salvation. This is why evangelization is so important too; because we can never know for certain that anyone else but a Catholic are on the path to salvation. And indeed, if we love someone, we want them to be on the path, don’t we?