I can't find any link between your Variables (vBookingFromDate, ...) and the according date fields you used as dimensions in your chart. So nothing will happen (this is correct) when selecting another value for your variable(s).
May be a calculated dimension will help you, similar to:
=if(date($(vBookingFromDate)) >= [Booking Start Date], [Booking Start Date])
instead of the simple dimension "[Booking Start Date]"
Same for "[Booking End Date]"
Don't forget to check "Supress When Null" for these dims.
See attached qvw. You were missing actions on the variable triggers.