(Using a Web API project)
Create project in VS2015 selecting "Create new Git repository" checkbox.
Click on Team Explorer Home toolbar button.
Click on Sync button.
Create repo in BitBucket.
Under "Publish to Remote Repository", click "Publish Git Repo"
Get URL to BB repo under Command Line link "I'm starting from scratch"
Paste then click "Publish"
Now click Sync, and with little or no indication of any progress you should see the files in BB.
You can change a file and check in then sync and it should appear in BB (or actually, I think you may need to put a change in, not sure)