Sounds as though it might be a bit more than the floor getting wet through showering. Have you checked any nearby pipes? Is there anyone who could call in whilst you are out, just to ensure there isn't a major flood?
I'd also call a local plumber to book a slot for tomorrow. Most would have an answerphone.
Depends where it is coming from I suppose. Hope the heater is an electric one - don't leave it on if you go out.
Had a similar problem when ds was small - water dripping through ceiling into hall down a wall , turned out to be from a corroded heating pipe. I went out and left it for an afternoon - wasn't much I could do about it anyway by staying at home ! Hopefully in your case, if it were caused by the shower - either inlet or outlet pipe, or faulty seal - it won't get any worse now because there is no water going through there but it might take a while to drain. Is it easing off ?
Thing to be most careful of is if water gets near the lights or electric sockets as they could fuse. We found it also caused wooden doorframes to swell and paintwork to crack. btw household insurance covered most of it, not the plumber unfortunately, but we also required patched ceiling and redecoration.
Landlord should have some sort of insurance to cover such eventualities( for carpets, curtains, fixtures etc )so don't worry too much unless it has affected your contents. However it didn't cover us for accidental damge by our tenants to a carpet, so such rental polices are not always comprehensive. You really should have your own stuff covered separately though.