Mystery of the Bible is presented in Ephesian 3:6

So both Jew and Gentle can partake in the Promise of the Gospel. So what is the promise Christ is speaking of. Paul covers them in his epistles. First and foremost, I believe it is;

1 Corinthians 15:1-4

Moreover, brethren, I declare unto you the gospel which I preached unto you, which also ye have received, and wherein ye stand; By which also ye are saved, if ye keep in memory what I preached unto you, unless ye have believed in vain. For I delivered unto you first of all that which I also received, how that Christ died for our sins according to the scriptures; And that he was buried, and that he rose again the third day according to the scriptures:

Faith and Faith alone

You must believe in these words by Faith and Faith alone. By Gods Grace you are saved and placed into the body of Christ. Salvation imputes much more and the Mystery below.

Ephesian 3 1-10

For this cause I Paul, the prisoner of Jesus Christ for you Gentiles, If ye have heard of the dispensation of the grace of God which is given me to you-ward: How that by revelation he made known unto me the mystery; (as I wrote afore in few words, Whereby, when ye read, ye may understand my knowledge in the mystery of Christ) Which in other ages was not made known unto the sons of men, as it is now revealed unto his holy apostles and prophets by the Spirit; That the Gentiles should be fellowheirs, and of the same body, and partakers of his promise in Christ by the gospel:

Understand the GOSPEL

To understand the GOSPEL, one needs to read the epistles of Paul, starting with Romans, the rest of Matthew thru Revelations. And then Genesis 1-11 to understand the origin of Sin. And then then the Jewish history and the Law, the rest of the Bible. To get a handle on what to read next, we need to talk and setup a reasonable reading assignment. Reach out to my comment section. and Checkout my many sources. And Pray for Guidance.

Whereof I was made a minister, according to the gift of the grace of God given unto me by the effectual working of his power. Unto me, who am less than the least of all saints, is this grace given, that I should preach among the Gentiles the unsearchable riches of Christ;
And to make all [men] see what [is] the fellowship of the mystery, which from the beginning of the world hath been hid in God, who created all things by Jesus Christ: To the intent that now unto the principalities and powers in heavenly [places] might be known by the church the manifold wisdom of God,

So what is the Mystery the Bible speaks of?

You pasted it. Look at Verse 6 This is part of the answer.

That the Gentiles should be fellow heirs, and of the same body, and partakers of his promise in Christ by the gospel:

Ephesian 2:11-13

Wherefore remember, that ye [being] in time past Gentiles in the flesh, who are called Uncircumcision by that which is called the Circumcision in the flesh made by hands;
That at that time ye were without Christ, being aliens from the commonwealth of Israel, and strangers from the covenants of promise, having no hope, and without God in the world:
But now in Christ Jesus ye who sometimes were far off are made nigh by the blood of Christ. For he is our peace, who hath made both one, and hath broken down the middle wall of partition [between us];

Ephesian 2:14

For he is our peace, who hath made both one, and hath broken down the middle wall of partition [between us]; Having abolished in his flesh the enmity, [even] the law of commandments [contained] in ordinances; for to make in himself of twain one new man, [so] making peace; And that he might reconcile both unto God in one body by the cross, having slain the enmity thereby:

EPHESIAN 4:15-16

But speaking the truth in love, may grow up into him in all things, which is the head, [even] Christ:
From whom the whole body fitly joined together and compacted by that which every joint supplieth, according to the effectual working in the measure of every part, maketh increase of the body unto the edifying of itself in love.

Ephesian 4:25

Wherefore putting away lying, speak every man truth with his neighbour: for we are members one of another.

Fellowship equals the Body of Christ, So what is next?

As you read on about new salvation you will see God has imputed much to you and an eternal set in the Body of Christ.

So, the Mystery in the Bible follows what God wanted to do since creation. Give all of mankind an opportunity to believe in Him as their God.