I often ride on the 'pennine bridleway' and thought about riding further on it; when i consulted my map, it's not all marked as a bridleway. Is this correct?

it's not all been consessioned yet (if that's a word)

So it's a new invention and will become a bridleway at somepoint in the new future. Does anyone know when>

lots of it is a bridleway, some isn't.

Does anyone know when

when all the objectors die 🙁

It's an ongoing project. the original aim was to have it open by 2009, but dealng with landowners is a complex matter, and when bikes and rights of way are involved people become intractable and it all starts costing lots and lots of money

at the moment, it's open from Middleton Top to somewhere around Settle in the Yorkshire dales, with the odd bit extra here and there

The web site provides lots of details

That is me on the bike! Honest…..

Is it like the National Forest?

fewer trees.

The websites your best bet.
Which area are you riding and how up to date is your map?
Eventually all the PBW will by bridleway status or above, it just may be that some councils haven't upgraded/dedicated the sections just yet.