What is an action (in one word) that makes you say "goodbye"?

Is there some verb that represents an action of "saying goodbye" ?

Example:

When you meet someone, you say hello.

When you ____ (with) someone, you say goodbye.

When a pair does this it is called "break up".

Solution 1:

The verb you are looking for is part

to go apart from or leave one another, as persons

[Dictionary.com, sense 23.]

In your case,

When you part with someone, you say goodbye.

Solution 2:

The verb leave could also work:

3

• a : to go away from : depart (leave the room)
• b : desert, abandon (left his wife)
• c : to terminate association with : withdraw from (left school before graduation)

When you leave someone, you say goodbye.