Not only you must copy them in your ~/.ssh folder, but you need to make sure:
they are named correctly:
id_rsa (for the bigger of the two files)
id_rsa.pub (for the smaller)
they are protected correctly
chmod 600 id_rsa*
Then you can copy id_rsa.pub
(make sure it is in one line) in your BitBucket account, ssh keys section.
Finally you can test if that is working with
ssh -Tv git@bitbucket.org
At the end, you should see:
logged in as <yourBitBucketAccount>.
You can use git or hg to connect to Bitbucket. Shell access is disabled.
That means you are properly authenticated, and will be able to push back to Bitbucket as yourself.
If you don't see that, the previous lines allows you to double-check what files are taken into account by ssh.