It depends on your TeamCity setup. Do you have it installed behind a firewall (can it be accessed publicly)?
The short answer is to set up webhooks. If your install is not publicly accessible, then you'll have to jump through some more hoops. Let me know and I can help either way.
It looks like I was slightly wrong. You'll need to set up polling to make this work (please make sure to set the poll interval to no less than 5 minutes).
These should get you going:
If you'd rather have builds triggered, you'll need something in between Bitbucket and TeamCity to receive the webhook and make the appropriate TeamCity API request (this could be done with an AWS Lambda).
Here's the info for that direction:
Lastly, you can jump in to this HipChat room if you want some more "real-time support":
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