This is what I believe the Lord showed me a few months ago when I had the same question as to why Elisha was bald. I studied the Bible using nothing but a Strong's Concordance to help me, after praying for discernment.

 

   Amos 8:10: And I will turn your feasts into mourning, and all your songs into lamentation; and I will bring up sackcloth upon all loins, and baldness upon every head; and I will make it as the mourning of an only son, and the end thereof as a bitter day.

 

   The following verse was written after Job discovered that his family had all died. Following this it says in all this Job sinned not:

  Job 1:20 Then Job arose, and rent hismantle, and shaved his head, and fell down upon the ground, and worshipped.

 

   So then we read in 2 Kings 2 the story of the day that Elijah and Elisha walked together for the last time. They had gone through the same towns earlier that same day and all the Bible says is the sons of the prophets came out to meet them and asked Elisha if he knew his master was going to be taken from him THAT DAY. There was no mention of anyone mocking him then, nor any mention of his being bald.

 

    Then we are told that the children were mocking him for being bald, and taunting him saying "Go up, thou bald head..." which could have been in reference to Elijah having already "gone up". The passage in 2 Kings 2 says that he tarried at Jericho after Elijah went up, that is when he healed the waters. So if he "tarried" he certainly had time to shave his head in mourning for Elijah, who had gone up.

 

   2 Kings 2:12 And Elisha saw it, and he cried, My father, my father, the chariot of Israel, and the horsemen thereof. And he saw him no more: and he took hold of his own clothes, and rent them in two pieces.

 

     Having read the verses in the Bible regarding baldness it looks like shaving one's head was a sign of lamenting, as of a death. It seems to go along with putting on sackcloth and ashes, and tearing one's garments as a sign of grieving. It also seems to have to do with shame. Elisha rent his garment, which was a sign of mourning, so I would think that the bald or shaved head was an additional outward sign that he did to show he was grieving over the loss of Elijah, whom he considered as a father, in the spiritual sense of the word.