An American student asked me how he should greet the Bishop when he visits.
Most Bishops nowadays are happy to be greeted as "Bishop "John" (or whatever his name is.) A more formal greeting which is still quite acceptable is "My Lord." For an Archbishop, this would be "Your Grace".
Many Bishops are a little embarrassed at you kissing their ring. However, they shouldn't be. This gesture is not meant to be some kind of fawning sycophancy. It is a recognition of his office as successor to the Apostles. Having said that, it is probably better not to kiss his ring if it makes him feel uncomfortable - unless you particularly want to make a point.
Occasionally, people from Catholic countries kiss my hand when they greet me after Mass. I don't try to stop them. It is not me they are respecting but the sacred priesthood. I'm not worthy of it and their reverence is a reminder to me of the need to try to live up to the grace of the priesthood.
My favourite example of the meaning of such reverence is in the film "Going My Way" - or it may have been "The Bells of St Mary's." Fr Chuck O'Malley (Bing Crosby) goes into the Bishop's study, kneels down and very formally kisses his ring. He then gets up and shakes his hand familiarly, saying something like "How are you John". He shows his reverence for the office first, then his personal friendship for the man.
By the Way, Bing Crosby got the Oscar for best actor for his performance in "Going My Way". The film got 7 Oscars all together. "The Bells of St Mary's" is also great - Ingrid Bergman stars in it too. Double DVD with both films £7.97 from Amazon.