I can only guess, without context. Following are some examples of how it could work:
Ay, matey! Whar ye headed?
(Hey, fellow, where are you going?)
Up the cove and around the horn! How 'bout ye? Whar's yer compass pointin'?
(Up the cove and around the horn! How about you? Where are you going?)
I agree with both your versions, Biblio and MJ. The version in my head was: Have you a cutlass 'bout ye, good knight? [Have you got a cutlass about your person ...?] (or are you just pleased to see me?)
I can vouch for the accuracy of the BBC in this respect, at least.
It is not a greeting I would use in formal contexts, or indeed at all, being a kind of formal kind of a person. But I have heard it often and it is the caricature greeting of the Belfast working man.
It is possible to buy mugs emblazoned with 'bout ye - in the tourist shops.
Just as every Australian wears a hat with dangling corks, every Scot wears a kilt, every American wears loud shorts and carries a camera, everyone in the south of Ireland says "Top of the morning"; so all of us in Northern Ireland say "'bout ye" as a greeting.
'bout ye is a greeting considered formal in northern ireland. it means something along the the lines of "hello, how are you?"
similar to "alright?"
used by most citizens of belfast, even me, and im only 11 and im a girl.