What is the function of a salt bridge?
Anions and cations do NOT flow, its the electrons that flow between the two beakers.
Eeectrons do not move in that described way either, they go from anode to cathode (negative to positive).
The salt bridge contains a salt solution, by doing this the electrons in the salt (ionic compound) are free to move, along with any electrons that wish to do the same. It also prevents equilibrium in the reaction. This is because, the salt bridge allows the electrons to flow back to the beaker they came from, i.e. it completes the circuit. Without the salt bridge, the electrons will have fully transferred giving each beaker either a positive or negative charge and therefore completing the reaction, and stopping the flow of electricity.