I've stayed in several different bedsits... they are usually a flat, divided up into smaller 'studio' flats.
You share the bathroom, and sometimes share the kitchen. But a lot of times they have their own kitchenette in the room.
You normally dont share a lounge, either... the lounge of the flat is usually converted into a room of its own. It doesnt make financial sense for the landlord to offer a shared lounge, when the lounge could be made into another bedsit, so more ££ for the landlord.
The last bedsit i had, my room had previously been the lounge. It was very large (old Glasgow tenement), and i had the big bay window!
There was (all in the same room) a single bed, a couch, a dresser, a wardrobe, a fridge, cooker & sink. So i think the studio apartment with shared bathroom is the closest comparison.
That's probably what you want to look for, Chelsea. The other alternative would be your own room in a shared flat.... that;s not called a bedsit, it's usually called a flatshare. It's usually where the owner of the flat is renting out bedrooms, so you would, in this case, be sharing a lounge, kitchen and bathroom. For me, that's not enough privacy.... i'd go for a bedsit, especially if it had a kitchenette in the room.