Wiring and programming a shunt with Arduino for 2 way current sensing
You need to offset your measurement to some reference, maybe half of your ADC range.  You can do this easily with a bi-directional current shunt amplifier:

One example is here: INA303

You would also need to generate a reference voltage, and supply that to the reference input of the amplifier.  Then, 0A is equal to the reference voltage and the output will increase with positive current and decrease with negative current.  Scale the gain appropriately.

You can feed the output of that into your AdaFruit A/D.  It's also possible to do the same thing with discrete op-amps, but the shunt amplifier parts are much easier to use.