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The best way to go about that would be to contact an electrician first and then discuss with him how much of the installation you could carry out. Problem is finding one who doesn't mind doing that.
I had a funny electricians rate sheet at one point which went something like :-
£50 to fix the problem
£100 if your mate already had a go
£150 if you had a go
£200 if you want to watchIt's tongue in cheek but of course there's some truth in there.
I don't want to get the big book out but it would make sense that an electrical installation in a bathroom would need signing off. If a new circuit was required it would definitely need signing off. Of course you can try and use the 3rd party scheme but you need amp electrician who'll agree to it.
Don't want to dampen your enthusiasm for it, I'm sure on a practical level it's not too difficult but you would need to properly check the insulation resistance of an installation like that before you commissioned it. Not just a bang test with the breaker!