group overal results by a relationship value

I have a table 'dates' which I want to return with('bookings'). The bookings table has a customer_id and that customer may be booked into several dates.

   public function bookings()
        {
            return $this->belongsTo('App\Booking');
        }

I am trying to count the number of customers that have booked between a date range. So, I want Date::with('bookings') then group the result set by bookings.customer_id.

I presume I can't do this with groupBy since it returns an array of all the dates with a single customer/booking per relationship.

i.e.

date1->bookings->[customer_id:5]

date2->bookings->[customer_id:5]

date2->bookings->[customer_id:3]

My brain is in a knot so if anyone can help that would be great!