I second what Royal just said.
As the coolant heats, it will expand and vent overboard (now that your overflow bottle is gone). When the engine cools and the coolant contracts, the radiator will suck air into the system. You will continue to lose coolant until you reach the point where the hot coolant volume equals the volume available.
At this point, the system will be full only when it's hot, and everytime it cools it will suck some fresh air into the system, bringing with it the oxygen that will hasten corrosion of your cooling system parts.
You need that bottle.
Loren