Multiplexing 2 digit 7Segment with one Bit
You are right about the NPN transistor, that is what you need in order to achieve that behaviour, however, since the µC would have to control the cathode of one of the displays, that would be a problem since most µC can only source / sink a few mA. Assuming each segment needs 10mA that would require the pin to sink 70 mA.

The most simple solution is to have two NPN transistors capable of sinking at least 100 mA (such as the common BC547).

Diagram bellow:



Being D1 and D2 the 7 segment displays (please ignore the reference). The anodes on the LEDs will connect to the µC pins.

In this configuration only Q1 conducts when the µC outputs 1 and when it outputs 0 only the Q2 conducts.

Note
It might be necessary to add a high value pull-up resistor (for example 100 kΩ) to the base Q2.