How long does it take to replace bottom bracket bearings? How long does it take to replace bottom bracket bearings? Is there anything that can make the procedure take more or less time? How does the type of mechanism affect repair time?
There are three main categories of bottom bracket, adjustable type, cartridge-style, and external-bearing. 

Cartridge-style bottom brackets are not serviceable, the replacement requires replacing the entire bottom bracket assembly. Removing the cranks and installing the new bottom bracket is a pretty straightforward task, and should take less than 20-30 minutes.

Adjustable-type can require a little bit of time to get the tension right, plus they are typically more difficult to remove due to the fidgetiness of lockring spanners and the fact that the fixed-cup is typically seized hard into the frame.  I'd allot ~45 minutes to an hour for that task. Depending on the brand of cranks.

External-bearing splits the difference - some have more steps  than cartridge bottom brackets, some are equally simple.

Note that in all cases, using the correct tools is important.