Bethlehem was part of the "land" of Jerusalem. See the link for more information, about half way down the page. 
 
http://www.lds.org/ldsorg/v/index.jsp?vgnextoid=2354fccf2b7db010VgnVCM1000004d82620aRCRD&locale=0&sourceId=661105481ae6b010VgnVCM1000004d82620a____&hideNav=1 
 
Also, this goes to show further proof that the Book of Mormon was not written by Joesph Smith, since one as acquainted with the Bible as he, wouldn't have made such a mistake. 
 
This further illustrates the point. 
 
"Joseph Smith, of course, knew well that Jesus was born in Bethlehem. If he had been the author of the Book of Mormon he would have so stated the fact, since any deviation from the well-known setting would certainly draw objection and accusation. However, Joseph Smith was merely translating a geographical note from an ancient writer—a note which in itself is another evidence that the Book of Mormon derives from a Semitic background.  
 
Thus, Alma’s prophetic preview of the setting of the Savior’s birth is not erroneous or contradictory. It is compatible with similar biblical and extra-biblical figures of speech—evidence, in fact, of the passage’s authentic ancient origin." 
 
Hope that Helps.

Also, when the term "Jerusalem" is stated, it means more than just the city itself, but rather in this context: 
 
"And Jesus was born of Israel."

Remember that when the Prophet Alma wrote this it was almost 600 years since any of his people had been in Israel. They have no clue of the geography of Israel at that point.  
 
Bethlehem is a suburb of Jerusalem with less than 5 miles from the center of one to the other.  
 
Would you expect Mary or Joseph to have detailed knowledge of the Americas? 
 
Of course the Americas? Do you know the name of every town in the Greater Beijing metropolitan area of China? 
 
Of course not, he used the name he knew to be closest and like the other posters have said even one as uneducated as Joseph Smith would know that Christ was born in Bethlehem not Jerusalem. 
 
If Smith was making a story up he would not of let such a simple error get through. But since he is translating a historical record from the Americas he has no ability to change what is written! 
 
I thank you for the question Josh! 
 
I hope my answer helps you!