The bipolar supply for opamps is to allow the output (and input) to swing above and below 0V. This makes many applications easier as AC signals don't have to have DC bias. As long as the input/output doesn't need to go lower than the negative voltage minus the output (opamps can only go within a certain voltage of either rail, for some this is ~1.5V, for rail-to-rail opamps this can be a few tens of mv) it will be fine.
Also note these charge-pumps can only output a voltage higher than the negative of the power supply. They also have fairly high output resistance - so the more current you draw from the negative rail, the higher (less negative) the voltage will go.
What opamp are you using? And what is the application?