Battery, switch, bulb

An AA cell, shown at 2× size, with a quarter cut away. Close the knife switch, or click its blade, and follow the charge.

What to notice

The wires are always full of electrons. Closing the switch moves them all at once. That is why the bulb lights instantly.
Real electrons here drift about 0.1 mm per second, slower than a snail. The animation speeds them up.
No electron crosses the separator. Inside the cell, ions carry the charge.
Electrons flow from − to +. "Conventional current" was defined the other way, before anyone knew about electrons.

Anode (−): Zn + 2OH⁻ → ZnO + H₂O + 2e⁻
Cathode (+): 2MnO₂ + H₂O + 2e⁻ → Mn₂O₃ + 2OH⁻