The main way in which a simple incandescant bulb ages is by evaporation of tungsten from the filament while the bulb is on and at normal operating temperature.
The specific way in which the filament is "consumed" is that the rate of evaporation is higher where the filament is hotter. Since the same current flows throught all of the filament, the filament is hottest where it's diameter is smallest, since a reduced diameter has a higher resistance per unit length. This means that the hottest spot, already the smallest, loses tungsten fastest, and becomes even hotter. ... etc.
Tungsten is fairly brittle at normal room temperatures, and is actually "tougher" at lamp operating temperatures. The current, as noted already, is much lower during operation than during the turn-on surge; so a weak spot that holds together for a while during steady operation may not be strong enough to stand the surge current at turnon. A filament that's "very near end of life" is likely to fail under the surge when turned on, hence the "folk knowledge" that turning the lamp on and off shortens its life.
The actual "using up the life" of the lamp occurs almost entirely during normal on-operation, and the life of a lamp is almost entirely the cumulative time spent turned on.
Turning a new bulb on and off has virtually no effect on the remaining life of the bulb. If the filament doesn't break it's not affected by the surge. It's only when the filament has been used long enough to develop local areas of reduced diameter that the turn-on surge can "pop the filament."
If the filament has degraded to the point where it could remain lit for another x hours if left on, but has a hot-spot that can't stand one more turn-on, then turning it off will lose that last x hours, since you can't switch it on without breaking the filament. (Unless you use a dimmer to bring it up without the surge perhaps?)
The time between when one more turn-on surge will cause the filament to fail and the time when it will fail if just left turned on can be a fairly significant number of minutes, or even a few hours; but isn't often a very large percentage of the total life expected.
For industrial lamps, and for some "long-life" ones, you may sometimes find a statement that "life" is based on a certain operating cycle, and a usual assumption is 8 hours on per 24 hours. This usually means that a "750 hour" bulb is expected to be on for a cumulative total of 250 hours.
The "gotcha" here, is that they almost never will tell you whether the "life" quoted is a mean, median, one-sigma, two-sigma, or another one of the several "statistical measures" that might be used, so they haven't really told you anything very meaningful.
They might mean that no more than 10% of bulbs will fail before the specified "life," or they might mean that "we had one once that lasted this long."
Casual experience, not rigorously measured, would indicate that about 60% of bulbs may last 3x the "life" on the package in normal service, and usually not more than 2 - 10% fail before you've used up the flavor promised.
Usual "business practice" is to turn off incandescant lamps whenever not needed, since power consumed leaving them on is significant and bulb life is almost completely unaffected.
For fluorescent lamps, the power required to "re-light" them is quite significant when compared to the power consumed by leaving them on, so recommendations are to turn off if not needed for some specific period. The usual spec is something around a half-hour to an hour of idle time, although I've known companies who said to turn off the fluorescents if you'll be out of the room for 10 minutes or more.
(Note that not all "maintenance engineers" are spectacularly proficient statistical analysts, but a very short idle time spec may be based on the assumption that when you think you'll be gone for ten minutes it usually ends up being two hours.)