Grouping Collection's Relationships together

Sorry, I'm not exactly sure how to title this question. I am making a booking platform where, a user can book an activity.

Each activity is available on custom set days, and each day has different time slots available, and each time slot as a limited number of spots.

A user can book only a single day at a time. In that booking they can select multiple time slots they want to book, and can select how many spots for each time slot they want to book.

To achieve this I have 3 models: Activity, Booking, BookingSpot

Relationships:

Activity->hasMany(Booking)

Booking->belongsTo(Activity)
Booking->hasMany(BookingSpot)

BookingSpot->belongsTo(Booking)

Booking has a field called date that determines what date the booking is for, and activity_id that determines what activity the user booked.

BookingSpot has a field called start_time and end_time (this is how I determine the time slot), and booking_id that determines what booking it belongs too.

I want to show a schedule for the activity. Showing each time slot that has bookings and the spots that have been booked.

Here is what I'm currently doing:

            // Get all bookings for a particular day and group them by the Activity.
            $query = Booking::select('*');
            $date = date('Y-m-d', strtotime($date));
            $queryDate = BookingSpot::select('booking_id');
            $queryDate->where(DB::raw("date(start_time)"), '=', $date);
            $bookingIdArray = $queryDate->orderBy('start_time', 'ASC')->get()->toArray();
            $bookings = $query->whereIn('id', $bookingIdArray)->get()->groupBy('activity_id');

This returns all the bookings group by activity, but each booking could have multiple spots each with different start_time

How do I make a new collection from this that contains all the correct BookingSpots, that is grouped by start_time?

Edit: Here is a little chart to try to visually explain

userA, userB, userC, userD, userF all made a booking for March 24, 2019 for ACTIVITY

Here is what i am currently able to do

MARCH 24, 2019
ACTIVITY---|---userA-|-1:00PM
           |         |-1:00PM
           |         |-2:00PM
           |         |-2:00PM
           |
           |---userB-|-1:00PM
           |
           |---userC-|-1:00PM
           |         |-1:00PM
           |
           |---userD-|-2:00PM
           |
           |---userF-|-2:00PM



Here is what I want to accomplish

MARCH 24, 2019
ACTIVITY---|---1:00PM-|-userA
           |          |-userA
           |          |-userB
           |          |-userC
           |          |-userC
           |
           |---2:00PM-|-userA
                      |-userA
                      |-userD
                      |-userF