Where in the Bible does it mention that every person has a guardian angel? The Bible talks about various angels such as Saint Gabriel and Saint Michael.  Where in the Bible does it mention that every person has his/her own 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.”