"Hi" in sign language
Hello! Hi!
Hearing: "How do you sign 'hi' in sign language?"
Deaf: (showing the signword in American Sign Language)

Hearing: (sheepishly laughing) I should have known. (Or, gesture facepalming hirself)
This scenario sometimes happens that Deaf people experience.
ASL signs for "hi"
Meaning: used as an informal greeting.
Pronunciation: Dominant hand with loose "B+thumb" handshape with palm orientation facing outward waves in neutral space. The movement can be just once, twice, or multiple, depending on the contexts.
The movement, number of repetition, intonation, and such that Deaf signers can convey a subtle variety of expressions and meanings, like "hi", "hello", "hello!", "hiiiii", and so on. They are context-dependent.
Contextual variation.
Baby signing "hi"
Hello! Hi!
When linguists study proximalization, they study how ASL-speaking babies and toddlers move their shoulders, elbows, wrists, fingers, and knuckles with control when they develop language in signing.
The video demonstrates how the toddler articulated "hello" or "hi" with the larger movement. Later, she would be able to control with more finer motors.
"h-HI-i" variation
In the 1980s, when a hearing person asked a Deaf native-signer, especially among teenagers, what the sign for "hi" was. The Deaf signers often reply this sign, what I will give it a gloss name as "h-HI-i" for the sake of writing.
The majority of hearing people used that sign while Deaf people themselves basically never used it with other Deaf signers in everyday life. But, they used it only with hearing teachers and staffers as observed in my deaf school in the 1980s.
Why? We don't know, but what one possible theory is the "us vs them" phenomenon or collectivist mentality in the context of history of hearing oppression. Think of the historical contexts in the 1980s when bilingualism was just beginning to enter the scenes of Deaf education across North America. Prior to the 1970s during the oppressive oralism which sign language was forbidden, hearing teachers slapped deaf kids' hands with a ruler, and so on. Then in the 1980s, natural ASL was "anglicized", messing up its meanings, grammar, structure, etc.
This sign is a classical example of some other signs with the similar "hearing accent". In the 2000s, I met a hearing man who learned ASL in the 1980s in the region but haven't used the language for a couple of decades. I recognized many signs that Deaf people typically showed what they didn't use in real life ASL conversations.
Vocabulary of greeting variations
The ASL sign what is glossed as HELLO isn't as commonly used as the "hi" version and its variations which can be translated into "hello" or "hi" in English, depending on the contexts.
Sometimes, a Deaf signer will sign HELLO what looks like a salute, when she/he hasn't seen hir close friend in a very long time. It's like "Big hello!"
Related signs: GREETING.
Now that same hearing person in the opening paragraph above is scared to ask "what is the sign for 'bye'?" to avoid being embarrassed hirself again. :D
Here you are safe to look up BYE, BYE-BYE, GOOD-BYE anonymously. :D