Yes, we use the Bible for our Bible study, and read from it, and memorize verses. However, with a 4 year old, and a 6 year old, I have always looked for a good Children Bible to get a narrative loyal to the Bible, not watered down, but a bit more flowing narrative for support.
The first Children Bible I bought, was Classic Bible Storybook, in an older edition. I then found this one in Spanish, Historias de la biblia ilustradas, which they have in different languages, and lately I found The Children Bible, which has been there forever, my friend and husband had this Bible when they were children.
But in our hs group a lady was giving Catherine Vos books for free, and I took them with the intention of giving them away if they were of no use to us. And let me tell you I absolutely recommend her three volumes on the Bible. Her text is full of Bible verses, and her narrative is loyal to the text, at least the first volume. Reading her volumes in conjunction with the Bible itself, make for a solid understanding of the Old Testament accounts. I recommend her books.
Plus volume two that had no image HERE. Or the three volumes together.