With all the new sites around chances are high one has little reputation on a site where one still has one question that could call for a bounty. It has been suggested before to use rep from another site to set a bounty so I don't repeat that here. My idea is instead:
One bounty-account where reputation received from awarded bounties (and only such!) can be put to and which can then be used on any other SE site to set new bounties.
This would support replying to bounty questions by offering a special kind of rep that can be used on other SE sites as well instead of only on the specific site, without meddling with the privileges.
edit Taking into account Pekka's answer regarding the potential unfairness on the need to have gained bounty-rep by bounties (which may happen seldom and cause too much competition), I suggest the following addition:
... Also, reputation up to the total amount of bounties previously manually awarded on one site can be "withdrawn" from that sites account to the bounty account.
That would also support the bounty system in total by encouraging users to set bounties on each site.
Now I know loosening this further would be allow to put rep from any site to the bounty account (maybe at some not-1:1 exchange rate)
, but that would render this feature-request into an almost-duplicate of Allow bounty to be set with reputation from another site?