A best friend would be happy for you. You have free tickets and going on a holiday good for you. A friend would be happy that you have such an opportunity whether she is a part of it or not.
To top it off you invited her - you didn't have to do that. It is unfortunate she cannot get the time off from work, but instead of being angry with you - she should be appreciative you invited her. You didn't have to invite her.
Does not sound like a true friend to me. Why not invite another new best friend - one that would appreciate the offer.