Is there any possible way to search and list the bountied questions separately in SE?
To list the current bounty questions, click on the featured tab.
On the current UI (2019) it's at
https://stackoverflow.com/questions (for example) where you'll see this:
There doesn't appear to be a way to limit the search though. There's no
hasbounty: keyword on the search page. Since September 2011, the
hasnotice:1 search option can be used to show bounty posts, but that also shows other posts with notices (deleted question).
Using combinations of advanced search operators, you can reach around 90%-95% accuracy:
hasnotice:1(bounty is considered a post notice, but there are more kinds of notices)
closed:0(show only questions which are not closed)
locked:0(exclude most common notice that isn't a bounty)
lastactive:7d..(questions active in the last 7 days, as bounty bumps the question)
Example for a full search term:
hasnotice:1 closed:0 locked:0 lastactive:7d.. - 438 results on Stack Overflow while there are 400 questions with bounties.)
Credits go to alexolut for finding the fourth option. :)
I would have put this as a comment on the answer from @Squatch but I have no rep on meta.stackexchange so I can't. So here goes; maybe it's better as its own answer anyway.
I think Squatch's answer is in the right direction, but is not specified sufficiently precisely; people may have downvoted it because of that. What you need to do is:
Go to the "Questions" section of stackoverflow by clicking the big orange "Questions" button near the top of the window
Then go to the "Featured" tab by clicking the tab; you will now see all questions with bounties, as far as I can tell (maybe "Featured" should be renamed to "Bounties"?)
Enter a search term in the search field at the very top right of the window, such as [java]; the previous list of questions with bounties will now be narrowed by that search term. There is nothing magical about the brackets around the search term; brackets do not mean "with bounty". (I think brackets just explicitly designate a tag, as opposed to other stuff you can type into the search field?)
If you enter a search term when you are not already on the "Featured" tab, you will not see only questions with bounties; you will then be doing your search in whatever other context you were in.
While I'm on that subject: The user interface for searching on SO is a bit odd, to me; since the search is apparently done within the current context (orange button and tab) being viewed, the search field should be positioned lower than those other user interface elements, not above them at the top right. A search field at the top right, like SO's, is naturally assumed to do a context-free website-wide search. It is also odd to me that "Unanswered" is in two places (as an orange button, and as a tab under "Questions"), and provides different things in those two places; that confuses me. Those complaints are somewhat incidental to this question, but I think they have helped to create a general aura of confusion about how to search on SO; I know I found it to be a barrier initially.