I think collectively, the answers above have already given a lot of breadth on this... the answers have all been good.
Few Additional Points:
1.) In order to be saved, we need to know certain things ABOUT Jesus... and this all has to come from scripture.
a.) We need to know we NEED Jesus... so we have to understand we're sinners that need to be saved.
b.) We need to know WHO Jesus is... that he is GOD INCARNATE, and so he has power to save us
c.) We need to know WHY he died... that his death was a substitutionary atonement for our sin debt.
2.) All of this information about Jesus, and salvation, and what it all means... this is all part of the basic gospel... and it's found in scripture.
3. When people reject the Bible, that is an act of rebellion: rebellion is the OPPOSITE of the attitude required for salvation, so this would make me very concerned of a person's salvation.
4.) Rejecting the bible is usually just a SYMPTOM of a larger SYSTEM OF BAD BELIEFS... it's usually a symptom that indicates a lot of other problems, including heart problems.
5.) It is "possible" for a person to be sincere, and sincerely accept Christ, and then to later be confused by bad teachers, and disregard the Bible... it's possible.
All you can do is talk to them, as Nehemiah mentioned above, and see what they believe about Jesus now.
If they no longer believe Jesus saves, or that he's God... then I would take them at their word, and assume they are not Christians.
All of the posts above were very good.
We've all dealt with people like this, so we all have some experience with it.
God Bless.
.