The bleed pressure is measured upstream of the APU bleed valve by a total pressure sensor.
The indication on ECAM is relative to the ambient pressure, so the ambient pressure must taken into account and this information is provided by one of the ADIRU's as soon as they're switched on and the air data part is available.
Take a look at the PRESS-page of the lower ECAM, the differential pressure indication also works as soon as the first ADIRU is switched on, same principle here.