Where in the Bible does it mention that every person has a guardian angel?

The Catechism of the Catholic Church teaches that there is a guardian angel for each person. It is well to recall that while the Catholic Church does not confine its teaching to sola scriptura, there is scriptural support for the teaching that angels are assigned as protectors. Angels engage in a variety of tasks as described in scripture, to include protection of the faithful. In English the term "guardian angel" is a way to describe an angel who protects someone.

The angels in the life of the Church

334 In the meantime, the whole life of the Church benefits from the mysterious and powerful help of angels.

335 In her liturgy, the Church joins with the angels to adore the thrice-holy God. She invokes their assistance (in the funeral liturgy's In Paradisum deducant te angeli. . .["May the angels lead you into Paradise. . ."]). Moreover, in the "Cherubic Hymn" of the Byzantine Liturgy, she celebrates the memory of certain angels more particularly (St. Michael, St. Gabriel, St. Raphael, and the guardian angels).

336 From its beginning until death, human life is surrounded by their watchful care and intercession. "Beside each believer stands an angel as protector and shepherd leading him to life." (203) Already here on earth the Christian life shares by faith in the blessed company of angels and men united in God.

St Basil notes this in his description of the distinction between spiritual beings:

(203) St. Basil, Adv. Eunomium III, I: PG 29,656B.
All the angels, having but one appelation, have likewise among themselves the same nature, even though some of them are set over nations, while others of them are guardians to each one of the faithful.

Scriptural verses that inform this teaching include:

Matthew 18:10

10 "See that you do not despise one of these little ones, for I say to you that their angels in heaven always look upon the face of my heavenly Father.

Hebrews 1:14

"Are they [i.e. angels] not all ministering spirits sent out to serve for the sake of those who are to inherit salvation?"

Luke 16:22

22 When the poor man died, he was carried away by angels to the bosom of Abraham.

Psalm 34:7

The angel of the Lord encamps around those who fear him, and he delivers them

Psalm 91:10-13

10 no harm will overtake you, no disaster will come near your tent.
11 For he will command his angels concerning you to guard you in all your ways; 12 they will lift you up in their hands, so that you will not strike your foot against a stone. 13 You will tread on the lion and the cobra; you will trample the great lion and the serpent.

Job 33:23-24

23 1 If then there be for him an angel, one out of a thousand, a mediator, To show him what is right for him and bring the man back to justice,

24 He will take pity on him and say, "Deliver him from going down to the pit; I have found him a ransom."

Zech 1:11-14

11 And they answered the angel of the LORD who was standing among the myrtle trees and said, "We have patrolled the earth; see, the whole earth is tranquil and at rest!" 12 Then the angel of the Lord spoke out and said, "O LORD of hosts, how long will you be without mercy for Jerusalem and the cities of Judah that have felt your anger these seventy years?" 13 To the angel who spoke with me, the LORD replied with comforting words. 14 And the angel who spoke with me said to me, Proclaim: Thus says the LORD of hosts: I am deeply moved for the sake of Jerusalem and Zion,

Tobit 5:17

Tobit said, “Blessing be upon you, brother.” Then he called his son and said to him: “Son, prepare whatever you need for the journey, and set out with your kinsman. May God in heaven protect you on the way and bring you back to me safe and sound; may his angel accompany you for your safety, son.”