3
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.
Only top voted, non community-wiki answers of a minimum length are eligible