Currently, the behavior is inconsistent. For most actions the user can always try to perform the action and if something is wrong, he's notified about it in nice big box of text.
For example it's not possible to vote on deleted posts. The vote arrows are still visible:
And clicking on any of them raise this friendly message:
Would be nice to have the bounty system work same way meaning the "start a bounty" link will always be visible and clickable; after clicking it, in case the bounty can't be started friendly message like the above will be displayed e.g. "You already have 3 active bounties" or "This question is less than 24 hours old" etc.
Another option is for this to be like the edit link: always visible, but disabled when can't be used, with the reason as tooltip: