Using two isolated secondaries of different voltages to power one device
With isolated secondary windings, your transformer should easily support making two voltage rails. Assuming that they are simple secondaries as I attempted to draw in the circuit editor, two rectifiers should work as diagrammed. Note that the voltages are just for reference, you won't see that exact voltage in practice.

The two diode bridges are used to create the desired common ground by connecting the negative DC output of the bridges together. This prevents the two secondary windings from being directly connected together. The bypass capacitors shown as C1 and C2 are also connected to this common ground.







simulate this circuit &ndash; Schematic created using CircuitLab

You do not want to put the secondaries in parallel or series. It would be possible to connect the 'bottom' leg of each secondary together and then use a single diode for each supply (as you pointed out), but then you would have significantly higher ripple for the capacitance you are using.

As a side note, since the windings are isolated and only connected through the diode bridges, it is simple to convert to, for example, +50V and -12V by reversing the diode directions D5-D8.