AFAIK, you need to have Git or Mercurial setup to work with BitBucket. After all, you will be making changes to your files. Please refer these links for further info on how to configure it with Jenkins.
Some detail from the link mentioned below:
Preparing the Jenkins project
Create a new project or configure your existing project that you want to hook up with your Bitbucket account:
a) Under “Source Code Management”, add your Git or Mecurial repository
b) Under “Build Triggers”, check “Triggers builds remotely (e.g., from scripts)” and add a really random string in the “Authentication Token” field. I’m now using KeePassX’s random password generator feature to generate the randomized and secure string
Before we hook it up with Bitbucket, we’ll need grab an API token from our Jenkins account:
a) Go back to your Jenkins main page, click on “People” link in the sidebar
b) In the People page, click on our newly created account’s entry
c) In our user page, click on the “Configure” link in the sidebar
d) Under “API Token”, click on the “Show API Token” button and copy that entry
Bitbucket + Jenkins = Bliss!
Now it’s time to hook Jenkins up with Bitbucket! Visit your desired Bitbucket repository overview page and click on the “Admin” tab
Under the repository’s admin page, click on “Services” at the sidebar:
a. Choose “Jenkins” from the “Select a service…” drop-down and click on “Add Service”
b. You’ll be presented four fields:
b1) Endpoint: Here, you’ll need to set your Jenkins URL in the following format — http://username:[email protected]/
b2) Project name: The project name that you’ve set in Jenkins
b3) Token: It’s the authentication token we created in Step 4
b4) Module name: (Optional) OK, this is one nifty feature that allow you to tell Bitbucket to only trigger a build when the commit contains file names that begins with a certain pattern
Ref: http://felixleong.com/blog/2012/02/hooking-bitbucket-up-with-jenkins