I've been in the flooring game selling carpets timber vinyl and ceramic tiles for 35 years, you are not the only one with this problem. The best solution is to remove the tiles but this is a big job but gives you 100% job but you probably know this. Bamboo flooring is good but please do your research on this because they are made two different ways Cold press and Hot press and the prices very from $30 - $60 also you will need to ask for the VOC certificate for things like formaldehyde. A lot of the cheaper suppliers do not have there's tested. The other thing that the industry is having but they want tell you is the bamboo is expanding and contracting a lot more in the Australian climate. Sorry to put a damper on bamboo. There is a newer floating floor on the market it has been around for about 7 years it is vinyl 4.5mm to 6mm thick its is good for going over tiles as it does not create to-much of a step and other issues in doors and kitchen

It can either look really dramatic or too dark, depending on the size of the room as well as your other components. I've attached a couple of images of our work using dark tiles, the smaller bathroom we have surrounded the bath with dark tiles but then balance it with an extra large mirror to bounce the light around the room. The larger bathroom we have taken the floor colour way onto the wall but used a different texture on the walls for drama. Hopefully this gives you more of an idea but you shouldn't to nervous of the room being dark, it's where you can create a contrast as well as textures. Look forward to seeing what you go with in the end.

The bathroom floor tiles which are shiny are the same in the shower unit which make it dangerously slippery. Is there a coating I can put on the shower tiles to make it less slippery?

Walk-in-showers are great for large bathrooms, but are problematic for small bathrooms. Even more so with a timber floor which does not comply with the regulations for waterproofness for wet areas. There are regulations in place that your waterproofing will need to comply with, as set out by the Building Code of Australia and Australian Standards (AS 3740-1994). You will need to do some research and speak to a professional as you are heading for disaster with the combination of a timber bathroom floor, a small bathroom, a walk-in shower, no waterproof membrane to protect the floor and no understanding of the legal requirements. Houses of the 1920's traditionally had tiled floors so I would be looking at one of my suppliers such as the Olde English Tile Company to help you source somethiing that is period appropriate and legal instead of timber floors. Olde English Tiles Best of luck, Dr Retro of Dr Retro House Calls