Manners require time, and nothing is more vulgar than haste.

Courtesy takes time, and the time is most of what it is. Greeting someone properly, waiting for them to finish, noticing that they look tired: none of it can be done at speed, because the whole message is that you had time for them. Hurry communicates the opposite whatever words you use. Rushed politeness reads as processing rather than meeting.

Given that, pick the two or three encounters in your day that deserve to be unhurried and protect them. Arrive at those with nothing queued behind you. Being fully present for three people is worth more than being briskly pleasant to twenty.