Even if it is not 2 days old yet, shouldn't it have the link that says "bounty eligible in ? hours"?
No; you only see that link on your own questions (the second question you mention is yours; I don't see the message there either). The bounty function is not that important and if you see that message on every new question you visit, well, it just isn't worth the whitespace it is taking.
If you happen to have one of my userscripts installed, you would see such a message (though its wording is a little different).