Is the word in the Bible? No, but like many other theological truths,the theology of the Holy Trinity permeates the New Testament. It has been a part of the Church's theology from the beginning. While there are a few groups who baptize in the name of Jesus only, most Christians practice trinitarian baptism as commanded by Jesus at the end of Matthew's gospel.
We can start with St. John,
God is Love.
Love is by definition relational. It requires more than one (unless you are a narcissist). There must be at least a Father and Son.
The Bible does not say that God began to love, after he created the world. The Scriptures say God is love. It is his essence. From before the creation of anything he was love itself.
St. Athanasius explain it using St. Paul,
...one God who is above all things and through all things and in all things. God is above all things as Father, for he is principle and source; he is through all things through the Word; and he is in all things in the Holy Spirit.
We also see it directly spelled out by St. Paul when he greets the people of Corinth,
The grace of our Lord Jesus Christ and the love of God and the fellowship of the Holy Spirit be with you all.
Here he uses God as synonymous with the Father.
As Christians we believe that all Divine action is carried out by the Father, through the Son, and in the Holy Spirit; from the creation of the universe to and beyond the end of time.
What does any of this mean for us now?
It goes far beyond sentiment, "God loves me." As the current Pope and his two predecessors have tried to remind us, because God is love, Mercy is also part of the very essence of God. St. John Paul added Divine Mercy Sunday to our calendar to call our attention to this attribute of God.
Our great problem is that we reduce Divine Mercy to human mercy. We see it as the opposite of Justice. Part of the great mystery of God is that justice and mercy in God are not separate but are one realty, two sides of the same coin, if you will.
So the next time one of us get the urge to say,"I demand justice," we must simultaneously ask, "Am I ready to give mercy." If we live in the Spirit and not in the flesh, we will not try to have one without the other.