First confusion on my side was about where exactly to set SSH Keys in BitBucket.
I am new to BitBucket and I was setting a Deployment Key which gives read-access only.
So make sure you are setting your rsa pub key in your BitBucket Account Settings.
Click your BitBucket avatar and select Manage account. There you'll be able to set SSH Keys.
I simply deleted the Deployment Key, I don't need any for now. And it worked