What is the Biblical basis for the concept that Jesus spent time in Hell?

He went to the Limbo of the Fathers which is part of Hell. The Nicene Creed tells us he descended into Hell and on the third day he rose again. The Limbo of the Fathers is where the Justified of the Old Testament resided until after the Resurrection.

Q: What are we taught in the Fifth Article: He descended into hell; the third day He rose again from the dead? A: The Fifth Article of the Creed teaches us that the Soul of Jesus Christ, on being separated from His Body, descended to the Limbo of the holy Fathers, and that on the third day it became united once more to His Body, never to be parted from it again" Catechism of St. Pope Pius X, The Fifth Article of the Creed

"Q: What is here meant by hell? A: Hell here means the Limbo of the holy Fathers, that is, the place where the souls of the just were detained, in expectation of redemption through Jesus Christ" Catechism of St. Pope Pius X, The Fifth Article of the Creed

Luke 16:23 tells us that the rich man went to a place called Hades. "And in Hell, he lift up his eyes being in torments" The Bible describes the rich mans experience in Hades as "being in torments".

Acts 2:27 clearly states that Jesus soul was not left in Hades and that implies his soul was there but was not left there permanently. Earlier in verse 24 of the same chapter the Scriptures gives a picture of what took place when Jesus was resurrected: NET "But God raised Him up, having freed Him from the PAINS of Death, because it was not possible for Him to be held in its power."

Before Jesus was raised he was bound in the pains of death that held him captive. Also Jesus making reference in Matt. 12:40 to Jonah as the example of His time spent in between the cross and his resurrection is quite telling.

"For AS Jonas was three days and three nights in the whale's belly; so shall the Son of man be three days and three nights in the heart of the earth."

Strongs(G#5618) defines "AS" in these terms: "just as, that is, exactly like"

Exactly how was Jonah's time in the belly of the whale?

Jonah 2:2 "And said, I cried by reason of mine affliction unto the LORD, and he heard me; out of the belly of hell cried I, and thou heardest my voice."

He chose to use the one example of three days in hell suffering.

Roman 10 and Luke 8 give an exact location of Jesus before His resurrection and that it is not a pleasant place that even the devils are begging not to go there.

Romans 10:7 "or, “ ‘Who will descend into the abyss?’ ”fn (that is, to bring Christ up from the dead) NKJV

Luke 8:31 "And they begged Him that He would not command them to go out into the abyss." NKJV

I can't dig up the scriptural reference right now, but it is my recollection that Jesus preached the Gospel to the souls of those already departed in Hades, which is what the creed refers to. It's not that Jesus in any way suffered in Hades, but that he went there and released souls.

Also, Hades is, in Greek mythology, a place where the dead reside and it's not certain that it correlates to Hell as we understand it, per se.

EDIT: The scripture reference is 1 Pet 3:19-20:

¹⁹ After being made alive, he went and made proclamation to the imprisoned spirits — ²⁰ to those who were disobedient long ago when God waited patiently in the days of Noah while the ark was being built.

YES, He did.

1 Peter 3:19-20 (NIV)

19 After being made alive, he went and made proclamation to the imprisoned spirits— 20 to those who were disobedient long ago when God waited patiently in the days of Noah while the ark was being built. In it only a few people, eight in all, were saved through water,

Those disobedient spirits are obviously in Hell.

Matthew 12:40 NIV

For as Jonah was three days and three nights in the belly of a huge fish, so the Son of Man will be three days and three nights in the heart of the earth.

There are all kinds of verses that touch on Hell being deep inside the earth, and we know that inside the earth is molten sulfur.

Acts 2:31 NKJV

31 he, foreseeing this, spoke concerning the resurrection of the Christ, that His soul was not left in Hades, nor did His flesh see corruption.

His soul went to Hades but it was not left there.

Ephesians 4:9 NKJV

9 (Now this, “He ascended”—what does it mean but that He also first descended into the lower parts of the earth?

Also referring to Jesus first descending to the inner earth before ascending into Heaven.

First, it's important to understand that a biblical understanding of hell is not as cut and dry as we might like it to be. That's another discussion.

Second, the Nicene creed, which is most widely used creed across Catholic, Orthodox and Protestant, simply says:

he suffered death and was buried.

with no mention of hell.

Third, any orthodox (that's orthodox with a lowercase o) understanding of the crucifixion includes that Christ died. In fact the shortest "creed" of sorts found in many Communion liturgies is simply:

Christ has died, Christ has risen, Christ will come again

The first part of that, "Christ has died", is really all we need to know.

If Jesus, fully God and fully man, died, that means a part of the Godhead/Trinity/God died. Think about that for minute, God died. (Yes, it's illogical) There was a cutting off, a separation ("My God, my God why have you forsaken me"). That separation is the essence of hell/Hades/the opposite of heaven. So, I don't think it matters whether or not Jesus traveled in some form or someway to a "place" that is "hell", He, by being cutoff, forsaken by the Father experienced "hell".