1985 BMX Mongoose ATP Pro bike?

Your bike is not a BMX, it is a mountain bike with no suspension. While it is a very good quality bike, it is doubtful that it is worth a large amount of money. Bikes like yours are great for commuting, they have rugged frames and mounting points for racks and mudguards. They could also be used for touring. However this bike is somewhat obsolete not having indexed shifting. For some odd reason on a bike of this quality, the wheels do not have quick release levers, so you require tools to remove the wheel in the event of a flat tire, an inconvenience. As well the rear wheel uses a freewheel rather than a cassette hub,so your rear axle would be more prone to bending or breaking. If the bike were in excellent condition you might get $100 for it,but most offers would probably be lower

1985 Bmx

ATB does NOT stand for a BMX bike. ATB stands for "All Terrain Bike". Not even close to a BMX bike. And it's not listed in Bicycle Blue Book either - at least I couldn't find it. https://www.bicyclebluebook.com/

And BikePedia doesn't go back that far. Rare? It isn't. Sorry. Value? How much will some sucker (prospective customer) be willing to pay? Although the frame & fork have some nice qualities (triple butted) it still has very OLD and outdated shifters & derailleurs.

Ask whatever you want for it. To me, it's a $50 bike at the very most if in pristine, showroom-like condition.

I suggest you learn the differences between a BMX bike & an all terrain bike. Or maybe you're just blind. $25 to $50 at the most.