In a galvanic cell, do the ions from half cell move into the salt bridge?

I know that ions from salt bridge move into the half cell in order to maintain electrical neutrality. But in my book it's also given that ions move from half cell into the salt bridge. 


For example, in a galvanic cell with $\ce{ZnSO4}$ and $\ce{CuSO4}$, zinc ions from zinc sulphate solution move into the salt bridge in one half cell and sulphate ions from $\ce{CuSO4}$ move into the salt bridge in the other half cell .


