[bts]

Personally I would use the "I'm sorry, but..." approach because I'd be legitimately sorry that I have to take conversation into an awkward direction for a moment. I think the direct approach, while some would appreciate it, is taking a bit of a gamble: there's too much of a chance the person could take it the wrong way.

[pistoriusp]

I have a theory, it may be way off, but are you an American?

[gdp]

Starting a sentence with "I'm sorry, but..." is a very British thing to do, in my observation (and Bill Bryson's, for that matter).