I've personally been involved in one, two, three questions with bounties which were effectively awarded plus two that were placed and not answered. Twice answering and thrice asking. And each time critical information only became available when the bounty was expired or about to expire:
In the first I was awarded the bounty and the period for doing so ended before I had actually managed to finish the answer. This delay was due to having to communicate with a co-author and also having to wait for computation to complete.
In the second the answer was only edited to completion in the grace period of the bounty after the bounty period of one week.
In the third I had seen the question before and pondered it. Then someone else posted an answer only 10 hours before the expiry of the bounty. Then I realized I could finish from that and I did, again during the grace period.
Every time the bounty period was uncomfortably short. I think this is due to differences the between the programming site and the math site, and the period of one week having been chosen with the programming site in mind. As of writing, the programming site has 18 times as many users, and 400 questions with active bounties for the math site's 90. So users of the math site are 4 times as likely to place a bounty. Furthermore, in the programming site of the 15 bounties that are nearest to expiry 4 (26%) questions don't have any answers and in the math site 10 (66%) don't. I take this as evidence that bounties in the math site are not effective. I think part of this is because in math it's common for questions to be both intractable and compelling, whereas in programming that's rare. Of course there's nothing that can be done about that, but I think that a part of it is that math questions simply take longer to answer in average.
For my personal use case, I like to browse the bountied tab so suppose I come across bountied questions randomly regardless of how much time they have left in them. That means I'm going to have a mean of 3 and a half days to come up with an answer should I want to receive the bounty. I think that's often not sufficient. If we think of another common scenario where one answer gives a partial result and another finishes, if the second person wants to receive the bounty they have a mean time to come up with the answer of only $\frac 74$ days.