Once the conversation is over and people have to go their separate ways, there are manners when it comes to saying goodbye.
Note that Koreans will consider someone very rude if he leaves without informing them he is doing so. For the rest, it is a question of the degree of friendship and social relationship.
Koreans only say anyeongikasaeyo to older people and to strangers with whom the relationship is not well established. anyeong is usually used when separating in the streets or in crowded areas.
However, if the relationship is stronger between two people, different forms of saying "goodbye" may be used. "You should come to my place some day", "let's have dinner some time", or "let's call each other" are all substitutes for anyeong, and therefore the traditional "bye" will be omitted.
Finally, other words can replace "good bye". "Get home safe", "go safely", "be healthy" etc. are all words that substitute bye.
In sum, if Koreans don't tell you expressions like "bye" or "see ya", anyeong or jal ka it's not because they don't like you, but because they have different expressions to say goodbye, expressions they will often not teach you in schools or when you ask them because they are not conscious of it.
*Also not that there are different ways to say "hi" when people meet for the second time on. The expression anyeonghaseyo is very formal and only used in formal contexts or when people meet for the first time.
Note that the answer for anyeonghaseyo is ne which may then be followed by anyeonghaseyo but that is not mandatory.
When meeting for the second time on, people will use expressions other than anyeonghaseyo or anyeong. pap mogossoyo? meaning did you have lunch/dinner can be a remplacement for "hi" and the expected answer is ne, even if the person did not have lunch/dinner yet, unless the two people formally established that they met to have a meal together. Other expressions like 일 다 끝났어요? (did you finish all your work?), 어디 가세요? (are you going anywhere?) or 누굴 만나세요? (are you meeting anyone) all remplace anyeonghaseyo. The expected answer to all these expressions is 네 (ne, yes).
Finally, note that any question with a rising intonation should be answered by "yes". That is:
-Is she pretty (rising intonation)
-Yes (no matter what you think)
-Does he speak good English (rising intonation)
-Is she pretty? (falling intonation)
-Well, you know...
-Does he speak good English (falling intonation)
-kind of but still...