I was wondering if there was any danger associated with an HID bulb bursting and no one being around to see it or know about it for a few hours. What are the chances it could cause a fire?

73 percent.

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Most .. or rather a majority of grow room fires are caused by a HID light FALLING.

Make sure your ballast is grounded and use a 15-20 amp breaker. Aside from the danger of the light falling and the bulb breaking there aren't many "dangers" involving HID.

Make sure your light is secure!!!

Create a good amount of heat though, and that could be dangerous... for your plants.

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Everything in Moderation...

This is why I like to use cooltubes......

If any thing that electrical if it falls , thats where the problem starts.
Hot tube , cold tube, cpf, anything thats powered by electricity that falls has a possibility of caussing a fire.
Always use gfi in the grow room, always hang with a good chain, always think safetyfirst, ALWAYS HAVE A FIRE ALARMS , SAFETY FIRST, GROWING SECOND, YOUR LIFE DEPENDS ON IT. enough shouting do not kill you self and outhers.