Why not just get yourself a set like this and pump the water out instead?
Joking aside, the base of these old wash tubs (as that's what they were sold as in their later days) wasn't all that strong, and certainly wouldn't stand the unsupported weight of an average adult human without buckling and subsequently parting company with the 'crimped on' metal sides. I think you'd need a good, thick (double 3/4 inch + ?) sheet of marine ply under the base to support it, and probably some form of rubber sheet between the two to take up any play between them? Even then, I wouldn't want to risk it in terms of potential for leaks. After all, bolting the bath to the supporting timber to fix it securely is going to the leak potential, and leaving it free is going to allow movement and put strain on the plug hole seals.
Then there's the irregular shape of the tin bath, unless you run a shower curtain around the bath to direct the shower spray into it (and you're thin as a rake to move around freely within such a confined space without the clammy shower curtain sticking to you) then you'll most likely have water going all over the place, and potentially running between the sides of the tin bath and any surrounding trim, which will cause mildew, rot and associated bad smells.
To be honest, while it seems a nice retro/industrial architecture idea, in practical terms I think you'd be better with a more conventional and purpose made shower tray/cubicle?