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?
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!