[untested] I think it's probably because it seems you haven't set a reference to the bxslider. That's why you can't call the methods.
//hold a reference to the slider
var myBX;
$(document).ready(function(){
myBX = $('.bxslider').bxSlider({...});
}
//later on...
$(#yourPhotoFusionButton").on("click",function(e){myBX.goToSlide(4);});
Look up the public methods here: http://bxslider.com/options