Lets start with the pressurisation auto fail - a bit of a red herring I think.
As the above poster has pointed out, this may have been a function of cabin alt rate too high or cabin alt to high. The CPC is designed to swap for any of these occurences, and is not really a system failure in the above case, but rather 'user error'
The CPC BITE will show the reason it failed itself.
Bleed Trip is caused by either a high pressure (220psi) or high temp (490F). Bleed snags on the NG are notoriously difficult to identify, and Boeing have issued numerous service documents to assist maintenance in identifying the causes.
In this instance my money would be on a high pressure bleed trip, caused by the high stage valve that has failed to close fully.