I feel it should be FALSE as we can have a graph with n vertices and 0 edges ( it is still a bi-partite graph ) ,Here since no two vertices are adjacent,the graph is 1-colorable.
EDIT :
Difference between K-colorable graph and K-chromatic graph :
http://mathworld.wolfram.com/k-ColorableGraph.html
So every Bi-partite graph is 2-colorable,which means every Bi-partite graph can be proper colored with 2 or less than 2 colors. We can also say that every graph is 3-colorable or 4-colorable ...and so on,but every Bi-partite graph is not 1-colorable.
But every Bi-partite graph is not 2-chromatic or chromatic number of every Bi-partite graph is not 2 always because A trivial Bi-partite graph (graph with n vertices and 0 edges) is 1-chromatic.
NOTE : A graph is said to be k-chromatic if the minimum number of colors needed to proper color a graph is k.
A graph is said to be k-colorable if the number of colors needed to proper color the graph is k or less than k.