Well Doug, here in deepest Norfolk, people always used to say things such as, "Oim orf now, so chair-ee-oh mawther!" The Singing Postman sang "Cheerio" in one of his songs, ("Hev yew got a loit boi?'). 'See ya later' is a new expression to me.
In West London as a child, I often heard people say, "Ta-da!" for 'goodbye'. On Wheeler Dealers (car programme on TV) Mike Brewer always ends the programme with that word.
Cool, eh? (hee hee)