Assuming the jar is airtight--
I think your oxygen consumption rate may be too high and that 40$\mu l$ per hour$^1$ might be closer but since it's a high figure anyway we can use it. 40 $\mu l$ per minute would be about 2400 $\mu l $/hr.
A 12-ounce jar is about 0.355 liters. At sea level, air contains about 20% oxygen so the volume of oxygen in the jar is about 0.0709 liters.
At altitudes which are considered high for humans (17000 feet or higher) the percentage of oxygen falls to about 15%. If a bee is able to get 2400 $ \mu l$ of oxygen per hour from a jar, the volume of oxygen will fall to about 13% after ten hours.$^2$
Based on oxygen consumption alone I think a bee would be stressed at this level, especially at temperatures exceeding 32C. I would guess the bee would be stressed well before this, maybe after 5 hours (16.6% oxygen). If we factor in the likelihood that the bee's respiration is up due to the agitation of confinement I think we can shave another hour off.
Depending on the age, size, species, variety, temperature, location, etc. I think an outside limit of 4 hours in an airtight jar is a good guess.
Toxicity from CO$_2$ may be a problem but bees have a much higher tolerance for CO$_2$ than humans, according to one set of entomology notes. At 0.04% the concentration will only increase marginally due to a drop in oxygen alone but the bee itself will produce CO$_2$ and in far greater quantities under stress. A chart here shows production of CO$_2$ in reaction to a light being turned on. 400 ppm is 0.04% but in this case it is due to the bee. If the bee during respiration returns CO$_2$ as quickly as it consumes oxygen the jar could reach 7% CO$_2$ in four hours, a level that may be toxic for humans. But we have already suggested the bee is under stress from oxygen depletion at that point.
There are many assumptions in this note. A conservative estimate might be an hour in an airtight jar. I would not bet on more. There are probably other issues I haven't thought of. Bees are very fragile and the chart linked above suggests they would not fare will in such an environment.
$^1$ Respiration of Worker Honeybees of Different Ages and at Different Temperatures, Allen, 1958, J. Experimental Biology 36, 92-101. At page 97 Allen gives a chart showing log $\mu l$ $O_2$/mg body weight/hr. For a 14-23 day old bee at 32C he appears to give about .5 which means 1.65/mg/hr or about 115 $\mu l$ per hour for a 70mg bee. It may be a typo or perhaps I am misreading the chart. Also the study uses an older method of measuring respiration.
$^2$ This is a simplification. The bee will start breathing a mixture containing falling oxygen levels and this may slow the oxygen depletion a little. But if we say the bee needs what it needs this saves us a differential equation.