I just cleaned my bike with low pressure water but I don't have any lubricant. I left it to dry in my basement with the window left open.
Is there any chance my bike will malfunction or rust before tomorrow when I buy some lubricant?
No, of course not. Having your bike wet and unlibricated for one day won't damage it in any way. Washing it and letting it unlubricated for long period of time will cause you some issues. But one day is not a problem...
Spraying a bike with water doesn't actually remove all grease that exists on the chain and similar otherwise unprotected surfaces. So letting it dry off for a day is fine. Even letting it stand for weeks is fine, if it is stored in a dry place with no condensation.
However the situation is different if you actually do remove all lubrication from an unpainted surface (with a solvent or perhaps even abrasive, for example to prepare for a paint job or heavy maintenance). Then you need to dry it off immediately or apply rust protection to prevent it flash rusting.
As any others have said, nope, nothing will reeeaaallllyyy happen. The only thing you need to worry about is if the water sits for too long on parts such as your chain. Just make sure you buy proper lubricants, and NOT WD40's spray can!!!! ;)
Also, if you plan to do that often, it's best to just get a cheap rag and wipe the bike down to dry off most of the water first. Stops the water sitting in places that it probably shouldn't be in!
An easy way to get excess water off it is drop it a few times, the height obviously depends on the type of bike it is. Full suspension mountain bike you can give it a good old drop from a couple of feet, but a couple of inches should get most of the excess off.