I have one, heavily modified, which I keep partly for its novelty value.
It is certainly a bike for gentle pootling rather than serious riding. The comments upthread about its flimsy build are fair. I wouldn't pay more than £50 for a second hand example. A serious limitation is that the headset contains nylon components and these are the old standard thread pitch and so they are difficult to upgrade.
Modifications: I hacked the handlebars to create a conventional stem and flat bar arrangement then upgraded the apalling brake levers. To lighten it, I swapped out the 3 speed steel rimmed rear wheel for a modern alu rimmed single speed wheel. (I rode it as fixed gear for a little while using a 12 tooth sprocket). It is fun to ride though and remarkably smooth. My next job will be to rebuild and reinforce the head 'tube'. It was, and is, remarkably light for a folding bike, at around 10kg. I keep it for train journeys that will have a short cyle ride the other end.
History: Bickerton attempted to market in USA where his original design fell foul of a law that required bicycles sold in the US to have a top tube. Bickerton retrofitted a very short tube to triangulate the seat tube and the main tube, to meet this requirement. Later a design overhaul was undertaken by a Californian man by the name of David Hon who constructed his bike from steel and named it the Dahon Bickerton. A generation later his design has droped the Bickerton suffix.
Or something like that.
Design: the component that connects the handelbar tothe steerer is very interesting. It is a peice of machined aluminium bolted directly to the steerer, the other end of which grips the handlebar. Nowadays we recognise a stem like this as the basis of the threadless headset... but this was 25 ish years ago.
Another good feature is that the hinge is on the right of the main tube which means the drivetrain ends up up the inside of the folded package, a feature that Dahon has not retained on its modern bikes, unfortunately.
The Bickerton design allows the bike to be set up with a long reach, something I value. A too short top tube is a failing of the modern Dahon and IIRC the Brompton.