According to some dictionaries I checked, we have to use a preposition or an adverb with the word "drip" if we use a liquid as the subject like in "The water dripped down the wall". On Collins dictionary though, it says we don't have to use a preposition or an adverb and the example sentence for it is, "Amid the trees the sea mist was dripping." So I wonder if it is only an idiom or if we can do this with other subjects than "mist" too. For example, let's say the water is dripping from a bottle someone is holding. Can we say, "Hey, the water is dripping!" to that person without using an adverb or a preposition; or do we have to use a preposition or an adverb with "drip" in the sentence like in "The water is dripping from the bottle"?
I am a native of the United States.
Spoken English almost never requires the addition of prepositions or adverbs when using words referring to fluids such as drip and mist. This is most especially true when the source either is, or is believed to be, obvious. It's more common to find prepositions and/or adverbs when the destination of the drip is important. For example,
"Watch out! There's water dripping."
"Watch out! The pipe's leaking."
would both be used in the same circumstance, to indicate water is dripping from a broken or maladjusted pipe. On the other hand,
"Something's dripping on my head!"
are not equivalent because the second example would, without specific context, be used to indicate the source of a problem, not the consequence of a problem. Said another way, the first example would cause the hearer to look at the speaker's head while the second would usually cause the hearer to look around for the source of the leak.
The same rules would generally apply in written dialog, but in narrative it would be more appropriate to use the rules you've found in the dictionaries.
As Sally walked through the abandoned subway tunnel, she could see water dripping from long ignored water mains and hear more dripping further down the tunnel.
This is important because a reader, unlike someone standing next to a speaker, is unable to ascertain the source of the drip (or the context of the statement). Thus, it must be provided in the narrative or the reader could suffer confusion.
Please understand that writing styles differ from one author to the next, and "book English," while preferred for writing reports in school and technical writing, is often much more malleable in prose. The rules you find in dictionaries are the beginning of wisdom. Thank you for using them and bringing that experience to your question!