Just a personal view:
Bike is clearly a good medium in which to read a report on events now due,
but I would tend to delegate the chronometry to an external engine.
Perhaps a date-triggered Keyboard Maestro macro which adds a “due now” report to a Bike file ?
Longer term, my understanding is that Bike may acquire style sheets – allowing formats dependent on attribute values.
That may enable a pattern which is currently possible in TaskPaper with date-valued tags and some help from Keyboard Maestro or Hazel – colors indicating how close a date is getting: