Nice question, love it! I've found some information on reddit. Someone asked,
[I am] wondering what happens if my network goes out. Can the lights and switches operate without the Bridge?
The answer given was,
No. The bridge is essential to controlling the lights. Without a bridge they are "dumb" lights that merely invoke their default behavior when powered on: bulbs to a warmish white light and light strips to their last activated colour.
Without the bridge any kind of color control, or any other behavioral control whatsoever beyond turning on/off by flipping the light switch or unplugging, is entirely unavailable.
The bridge is the brain of the operation. The bulbs just receive instructions from it; they have zero intelligence of their own. Your smartphone can be used to program/control the bridge, but cannot in any form address the lights directly: they speak a different protocol altogether from wifi called ZigBee.
In other words, the light does not know the schedule; it is very much the bridge that sends the instructions to the light. The light is basically an endpoint in the system with no intelligence of its own: it depends on the Bridge system to turn it on and off.