H-bridge is the magic word. But, there is a BUT ...
Building this circuit with discrete devices you will have to make absolutely sure, that certain conditions won't happen if you don't want to fry the transistors in the circuit. As the transistors need a time (ok, pretty short, but they are fast) to switch from ON-OFF or OFF-ON you might run into a situation where the current is shortened through two transistors with any load in between which will fry at least one, maybe both transistors.
There for my recommendation is to use a special IC for that which is designed to avoid that shortening situation. A suitable H-Bridge IC is the L293D, which is pretty common in the Arduino world and pretty cheap, coming with internal protection diodes and it's inputs can be directly connected to the Arduino outputs without addt'l resistors.
The following links give you some more detailed information how to use the circuit; in your project just replace the motor with the single coil of your latched relay - polarity of the coil is irrelevant as you can switch the state back and forth by the Arduino.