The Credentials Binding Plugin is what you need to use. This can inject these as environmental variables in your Jenkins job scripts:
git clone https://$SECRET@bitbucket/scm/project/repository.git
This works with files for ssh keys as well, so you can now script your password and keys into your scripts. A service account with access only to what it needs to would be the best way to support this and you have those access credentials as safe as your jenkins master is.,