What is the biblical basis of the belief that Earth is the center of the universe?

The verses most commonly encountered during discussions of Bruno and especially of Galileo Galilei are included here.

Josh. 10:13 "So the sun stood still, and the moon stopped, till the nation avenged itself on its enemies, as it is written in the Book of Jashar. The sun stopped in the middle of the sky and delayed going down about a full day."

If the sun and moon miraculously stood still, then the ordinary behavior of the sun and moon ought to be movement. The heliocentrists argued that the sun was motionless and it was the Earth that moved.

Psalm 19:1-5 "The heavens declare the glory of God;
the skies proclaim the work of his hands.
Day after day they pour forth speech;
night after night they reveal knowledge.
They have no speech, they use no words;
no sound is heard from them.
Yet their voice goes out into all the earth,
their words to the ends of the world.
In the heavens God has pitched a tent for the sun.
It is like a bridegroom coming out of his chamber,
like a champion rejoicing to run his course."

Psalm 93:1-2 "The Lord reigns, He is clothed with majesty;
The Lord has clothed and girded Himself with strength;
Indeed, the world is firmly established, it will not be moved.
Your throne is established from of old;
You are from everlasting."

Psalm 104:5 "He established the earth upon its foundations,
So that it will not totter forever and ever."

Isaiah 40:22 "He sits enthroned above the circle of the earth,
and its people are like grasshoppers.
He stretches out the heavens like a canopy,
and spreads them out like a tent to live in."

These verses in Psalms regard the motionlessness of the earth as a testimony of the steadfastness of God, or the movement of the sun as a sign of his power.

Ecclesiastes 1:5 "The sun rises and the sun sets, and hurries back to where it rises."

A literalist might argue that this verse implies that it is the sun that moves about the earth, which is apparently the position taken by the contemporary Church. An educational website about the trial of Galileo includes this offical statement:

A decree of February 19, 1616, summoned Qualifiers of the Holy Office and required them to give their opinion on the two following propositions in Galileo's work on the solar spots. (The assessment was made in Rome, on Wednesday, February 24, 1616.) Proposition to be assessed:

(1) The sun is the center of the world and wholly immovable from its place.

Assessment: This proposition was unanimously declared "foolish and absurd. philosophically and formally heretical inasmuch as it expressly contradicts the doctrine of the Holy Scripture in many passages, both in their literal meaning and according to the general interpretation of the Holy Fathers and the doctors of theology."

(2) The earth is not the center of the world, nor immovable, but it moves as a whole, also with diurnal motion.

Assessment: This proposition was unanimously declared "deserving of the like censure in philosophy, and as regards theological truth, to be at least errouneous in faith."

It appears that while this statement may reflect the official position of the Church at that time, it was not universally held among those educated in the scriptures, even among priests of the Cathoilic Church. The same educational website includes this 1616 announcement of suspension of the publication of certain books that contained teachings, theological, philosophical, or otherwise, that were contrary to their previous statement that heliocentrism was contradictory to the Holy Scriptures. (bold added)

And whereas it has also come to the knowledge of the said Congregation that the Pythagorean doctrine—which is false and altogether opposed to the Holy Scripture—of the motion of the Earth, and the immobility of the Sun, which is also taught by Nicolaus Copernicus in De revolutionibus orbium coelestium, and by Diego de Zuniga [in his book] on Job, is not being spread abroad and accepted by many—as may be seen from a certain letter of a Carmelite Father, entitled Letter of the Rev. Father Paolo Antonio Foscarini, Carmelite, on the Opinion of the Pythagoreans and of Copernicus concerning the Motion of the Earth, and the Stability of the Sun, and the New Pythagorean System of the World, at Naples, Printed by Lazzaro Scoriggio, 1615: wherein the said Father attempts to show that the aforesaid doctrine of the immobility of the sun in the centre of the world, and of the Earth’s motion, is consonant with truth and is not opposed to Holy Scripture.

Modern positivists like to use heliocentrism as evidence that the Church is dogmatic and incapable of adopting empirical understanding. However, it is notable that the geocetric view was held by the vast majority of astronomers and educated people in general at that time- Galileo delayed publishing his own work on heliocentrism because he anticipated ridicule from his peers, not from the Church. The observable evidence that the sun is the center of the universe, stellar parallax, was not observable by instruments at that time and so most contemporary astronomers dismissed heliocentrism, at least initially, on scientific grounds. In fact, Galileo was guilty not only of insubordination to the Church authorities but of bad science- he was teaching that his theory that the sun was the center of the universe was true dispite the fact that he lacked the evidence to demonstrate such.

As far as the Catholic Church is concerned, these verses are not considered to be a valid Biblical basis for geocentrism. From Catholic Answers,

Unfortunately, throughout Church history there have been those who insist on reading the Bible in a more literal sense than it was intended. They fail to appreciate, for example, instances in which Scripture uses what is called "phenomenological" language—that is, the language of appearances. Just as we today speak of the sun rising and setting to cause day and night, rather than the earth turning, so did the ancients. From an earthbound perspective, the sun does appear to rise and appear to set, and the earth appears to be immobile. When we describe these things according to their appearances, we are using phenomenological language.

The phenomenological language concerning the motion of the heavens and the non-motion of the earth is obvious to us today, but was less so in previous centuries. Scripture scholars of the past were willing to consider whether particular statements were to be taken literally or phenomenologically, but they did not like being told by a non-Scripture scholar, such as Galileo, that the words of the sacred page must be taken in a particular sense.

According to Wikipedia, the Roman Catholic Church via Cardinal Giovanni Mercati made a statement regarding Bruno's condemnation in 1942, saying that the condemnation was just.