Dear LIB: how do I tell someone they have mouth odour without offending them

As sent in by a LIB reader

I love my girlfriend dearly but she has mouth odour making kissing her and having long conversations with her very difficult. I love kissing a lot but because I don't know how to tell her my reservations, I just tell her I don't like kissing to avoid kissing her. What do I do as I am thinking of ending the relationship