Like others here, I'm confused!
Portsmouth Airport closed in 1973, with the Anchorage Park development later being built on the site.
The nearest airport to Portsmouth is now Southampton. The only domestic flights from Southampton are to Aberdeen, Belfast City, Cardiff, Edinburgh, Glasgow, Leeds/Bradford Manchester and Newcastle.
There are no domestic flights operating to or from Liverpool airport.
So the nearest flights for you would be from Southampton to Manchester, with rail journeys needed at either end (unless, of course, you'd got a car available to you). Those flights are operated by Eastern Airways, who DO accept a bus pass as valid ID. (Here's a screenshot from their website:
https://ibb.co/2YSj465 ).
Flights on that route are typically around £80 each way:
https://www.easternairways.com/
Getting to Southampton Airport Parkway by rail requires a change at Southampton Central. There are direct trains from Manchester Airport to Liverpool Lime Street:
https://www.nationalrail.co.uk/