I've only opened one bounty before and it was closed. Now I am trying to open a bounty on several old questions (or at least see if I have the ability to do so), and I do not see that option. I thought the only things which blocked you from opening a bounty were having 3 open counties or trying to open a bounty on a question which is less than 48hrs old.
You're right, you can't place bounties on new questions or have more than three open bounties at a time.
However, you also need 75 reputation before the system will let you place any bounties at all. As I'm writing this, your rep is at 61, so you're still a few upvotes short.
For all the details, see the network-wide community FAQ page on bounties.