I am making a cake and filling in between the layers with bettercreme.  After I fill it I will cover it with ganache and then fondant.  Can this sit out after I put the fondant on Thursday, until Saturday?

If you actually mean BetterCreme, the non-dairy/whipped out of a carton, product, it is shelf stable at room temps under 80F for up to 5 days, so yes, it will be fine.

If you mean buttercream, it will depend on the recipe.