An instrumentation amplifier circuit (seprate OP-amps or a ready made chip) is a good way. For the zero shift, just have the reference point at 1.6 V.
With only a gain of about 1.6 the common mode range may be an issue and it may not be worth to use the full 3 OP-amp circuit.
Depending in the use, one could also have only a half bridge and have the 2nd half already as part of the amplifier.