getting values from a shortcode with an include

by

include changes the scope. You would need to declare $classslider global before defining it, and then use global $classslider; before using it. 

function bf_shortcode_slideshow($atts) {
  global $classslider;
  extract(shortcode_atts(array( ...

I think that will fix your problem.

I don”t understand why you are using include at all though. There must be a better way to make that slideshow work.