Why is there no salt bridge in electrolytic cell?
Electrolytic and galvanic cells have separation of electrolytes for different reasons. In galvanic cell you wouldn't have current if you mix electrolytes from both cells. In electrolytic cell you can dip both anode and cathode in the same solution. Then yes, you don't have a salt bridge because you use the same electrolyte. 

Salt bridge passes ions at a certain rate that is not too high in order to prevent electrolyte mixing. In electrolysis you can allow mixing so you don't need a bridge.

In electrolytic cell you have two transports. Lets say you have Zn/ZnSO4 and Cu/CuSO4

(1) Electrons are flowing from more active (Zn) to more passive metal (Cu). This is essential for creating the electric electric current in the cell. In solution without a salt bridge you have constant concentrations of anion (SO4$^2-$). However, concentration of Cu2$^+$ is decreasing (Cu deposits on metal) and concentration of Zn${2+}$ increases (Zn dissolves). This creates charge imbalance that will quickly compensate difference in potentials of Zn/Zn${2+}$ and Cu/Cu${2+}$.

(2) You cave a salt bridge. It has to pass ions at a right speed. Not to slow and not too fast. If ions can travel too fast (no wall) then diffusion will mix electrolytes in two cells, copper will precipitate on both sides and there will be no current. If ions travel to slow (solid wall) then the charge difference on both sides of the electrolyte will prevent further current.

historically, it was just a piece of fabric between two compartments. Diffusion through it is slow, but drift along the electric potential is fast.