I'll confess that I had to google "bedroom fitter" to find out if it was a recognised occupation, and it appears that it is. Well, you learn new something every day. Surely you have "kitchen fitters" where you live? It's clear that fitting kitchens - with the combination of plumbing, electricity, gas and complex configuration of units in an often restricted space - is a specialised service. Kitchen firms usually offer design as well as fitting, and the people who install the units and appliances are called "kitchen fitters". The same goes for bathrooms. Bedrooms are obviously more straightforward. A bedroom fitter would presumably install fitted wardrobes with integral dressing tables and so on. But if a large company offers several different services, it makes sense that their employees might also specialise. The people who are qualified plumbers, for example, would be sent out to install kitchens and bathrooms, while the ones who are more skilled at carpentry would install units in customers' bedrooms. By analogy with "kitchen fitters", I guess this would make them "bedroom fitters".

I've never heard 'bedroom fitter" specifically, but yes, you have the idea, it's someone who installs furniture. It's more normally used in the context of bathrooms and kitchens where there might be cupboards, baths and so on that need to be installed in the room, attached to walls and plumbing, not just freestanding furniture that needs to be assembled. In fact you will sometimes hear people talk about "fixtures and fittings" meaning things that are fixed. In place in a house (carpets, lampshades, curtains, cookers) as distinct from "furniture". We don't think about this a lot, so don't worry too much about exactly what falls into each category. I've only ever come across it when renting places to live. There are companies that will recommend a whole package of furniture, shelves and supplies. The client buys them and the fitters show up with all the equipment in a van, take out the old fittings and fit the new shelves, cupboards, work surfaces, etc in place and assemble freestanding furniture like chairs and tables. I guess your bedroom fitter might do the same with curtains, lamps, decorations, wardrobes, beds and so on, I expect.

Frankly speaking, fitter is a person who works with metal details. It doesn't matter what kind of job he does. For example Bedroom Fitter - fitter who installs details for furniture or something else... bathroom fitter - fitter who installs details for bathroom's furniture or for toilets, sinks. You are right!)