In the Old Testament we can see at least two people that didn't seem to ever die: Enoch (Gen. 5:24) and Elijah (2 Kings 2:11). The Scriptures say that the first one was taken by God, and the second one was taken to the heaven by a whirlwind. Besides this, are there any indications in the Bible that these two never went to Abraham's bosom (Luke 16:22)?
Because John 3:13 says, "And no man hath ascended into heaven, but he that descended from heaven" (Douay) I am inclined to believe that they went to Abraham's bosom. That is the easiest interpretation of that verse without going through some severe theological hoops.
Additionally, and this is admittedly out of the scope of the question directly, but there is general theological consensus that the death of Christ "opened the kingdom of heaven to all believers." And while this is in the Te Deum, you can also find similar notions in Luther and Matthew Henry's Commentary.