How long will a light bulb work isf the glass shell removed? How long will a light bulb work if it gets its glass shell removed?
 A: This is actually a chemistry question: at the temperature of a filament, a violent chemical reaction (oxidation) will take place that destroys the filament very quickly.
The actual process is two-fold. The outer layer oxidizes, and the oxidation process is exothermic (it heats the filament more). The resulting inner conductor is now thinner, and the thinning is not completely uniform. A "thinnest" region will appear where the filament heats even more rapidly, oxidation speeds up, and you get runaway. Failure occurs when the thinnest part of the filament melts - you will see little drops of (previously) molten tungsten at the bottom of a cracked bulb.
In my experience this takes a tiny fraction of a second in normal atmospheric conditions. If the bulb started out filled with (pressurized with) gas (e.g. argon), it might take longer as oxygen first needs to displace the gas that is there - but even that is very fast (slower if there is just a crack in the bulb and gas has to diffuse in while argon is diffusing out).
If you want an answer in ms, I recommend that you re-post in the chemistry site; this is really about rates of reactions at high temperatures. Typical tungsten filament temperature can be as high as 3300 K (for an argon-filled bulb) while melting point is around 3700 K. Many chemical reactions double in rate for every 10 K increase in temperature (rule of thumb - depends on activation energy) so compared to room temperature the oxidation rate is roughly $2^{30}$ or $10^9$ times faster.
A: If you bust a light bulb when it's off, then turn it on, it will last around 5 seconds. If you bust a hot light bulb that has been on for a while, around 1/10 of a second.
