Often when you meet people on the street you may opt to say "Hi" and then be on your way. To my understanding this is not considered a rude behavior. It is also common to greet someone have a bit of small talk and then say goodbye.
I am looking for guidance at which point not saying goodbye would be still considered ok?
At which point it would no longer be ok to omit goodbye?
I was taught by Americans acquaintances or friends about basic do's-and-don't when I arrived in the US. All small greetings ("How are you?", "What's up?", "What’s going on?"...) or expressions that don't require an full answer or just have a predetermined answer, like "Good / fine, what about you?" or "I am fine, thanks; How are you doing?". This seems to be the norm : [ 1 ] [ 2 ] [ 3 ] [ 4 ]
When you see people walking down the street, these greetings are enough. When you stop and engage to a more deeper conversation, no matter how long it will be, saying "(good) bye" is appropriate and it would be rude to 'not end' the conversation in such a way.
According to all of the readings about etiquette in the US, there seems to be no more to do while walking and crossing paths with people you know enough to greet.
On the other way, there'a almost always a required closing sentence/word when you end a conversation / small talk / meeting, as explained by Candace Smith Etiquette or Confident English.
In your situation, if you stop and talk, I'd say that saying a nice word ("bye", "see you") is more than enough (but required) to be a polite way of ending the talk when you meet people in the street.
1 MIT -- greetings in the US (with a link to IPS, mylord !)
2 American Etiquettes -- How people greet
In my personal experience, what you've outlined in your question (either say "hi" and keep moving, or stop, chat a bit, and say "goodbye") is exactly right. It's fine to keep moving if you don't have time to chat, in which case it would be odd to say "hi bye". But you don't start a conversation of any length, and then just walk off without saying goodbye. That would be rude.
Of course, lots of "closing phrases" can be substituted for "goodbye": "bye", "cya", "I'm off", "gotta run", etc.
