I want to offer a bounty for my question and the start a bounty link is not there. Please help.
There was a previous bounty that ended less than 24 hours ago (as of this writing).
There is a grace period of 24 hours at the end of the bounty to give the bounty setter time to award the bounty.
As there can only be one bounty on a question at any one time I can only assume that this means that you can't start your own until the full 24 hours have passed.
This section of the FAQ explains how bounties work, but doesn't include the 24 hour grace period.