Earlier quoted context omitted.
Me too. Public repos github, private bitbucket.
Honest question: why do you need a central repository (SVN style) if it's a private repo? I tend to develop my own projects mostly on two different machines, and the core code management and synchronization doesn't need anything but git itself. Is it so you can use bug trackers etc?
It's a free offsite backup, and if you ever need to add another machine (or developer) to the project, your code is already sitting there on bitbucket. And you never need to worry about firewalls, NAT, one of the machines being off, whatever, because bitbucket is (almost) always up and accessible. And if you forget to push after working, or if bitbucket is down, you can still fall back to your existing workflow.
In addition, if you're doing anything web based, sooner or later you'll need to deploy to a sever out on the internets. Being able to pull from bitbucket makes deployment really easy, again without tinkering with firewall ports or anything.
It's not so much a question of "need" it's "why not do this thing which has some benefits, and no real downside?"