In the US it’s not uncommon for people to put the phone down or kill a telephone call without saying goodbye. It’s not considered rude. We’ve seen it on TV and film a hundred times. That’s not to say it’s not mildly unnerving to a European the first time it happens.
At the other end of the extreme are people that say bye multiple times at the end of a call. It’s as if they’d be terrified if the person at the other end didn’t hear them formally close the conversation, so they double- and triple-up to be sure.
I heard this staccato farewell a lot in Scotland when I lived there and you hear it a lot in Ireland. It’s a rat-tat-tat delivery of multiple byes that has a natural cadence of its own: 3 quick byes and 3 longer byes over a 3-second-or so period. Sort of a ‘ba-bye-bye [very short pause] bye-bye-bye.
I have a Belgian friend who always closes the call with a ba-baaaaaye, one short blast and a long blast, and then he’s done.
Me? I prefer a punchy ba-bye, that’s it. Simple, decisive, clear.