Datasheet figures 5 and 6 are discussing different kinds of single supply operation. I don't know which is better meeting your application. If you need a bipolar output signal, then IAref need to be connected to a positive "pseudoground" or virtual ground as in figure 6. The output will have an offset, but you can hardly remove it without losing the bipolar signal swing. If your signal is unipolar, but the signal has an unwanted offset, which would be originated from the input, an additional differential amplifier, as suggested by Alex, can help. But you should consider, that no single supply amplifier can achieve exactly zero output.
Another imnportant point with instrumentation amplifiers is keeping the input common mode range. Related to single supply operation of INA125 this implies a positive bias voltage to be applied to the inputs.