I think the main problem is she took it the wrong way.
When you said you were bi to her, it obviously meant you would be up for sex with boys or girls you wouldnt really ahev a problem with it. However since you came out with that she might have thought you meant the usual misconception that goes with bi people which is you are greedy, that you saying you are bi made her think you were going to try and get off with a guy as well as her.
You should bring this up and say if thats what she was worried about, to be honest it is a incredibly popular misconception about bis, I dont blame her for getting caught up thinking that way about it. Let her know you arent going to cheat on her but you are just more sexually open than being strait.
I doubt she has a problem with your sexuality as it is but just what she thought you meant. If you get it out of the way, both have a good laugh about it and have some good make up sex.
Give it a year or two ad she might even consider letting you have your bi way and have a threesome with another guy, fun for the both of you :)