I just got started with BitBucket (And am already loving it!).
I have a small problem. I have a "Managed" Firewall, controlled by an application (Specifically TinyWall). It's useful for keeping unwanted connections at bay, but of course, it blocks everything but what is whitelisted. I had the infamous Failed to connect to bitbucket.org port 443 error, which I assumed was my end, and disabled the external firewall for a bit.
Sure enough, that fixed the issue.
So anyways, on to the actual question: What process/executable manages the git requests? I'd like to re-enable my FW, and from the looks of it, that's a small fix.
So, on accident by messing around with Process Hacker, I followed the request attempt and found the source program.
As Theilo mentioned in the comments, it depends on what you are using to try and connect.
Below are the directories to the programs one may need to whitelist to your firewall if you are in a similar predicament. NOTE: These directories are likely to change as updates for their respected platforms occur. Another note: The issue is centered on windows machines. While the fix and troubleshooting are similar, expect differences when attempting on other platforms.
GitHub Desktop Client:
C:\Users\<INSERT USER HERE!>\AppData\Local\GitHubDesktop\app-1.0.9\resources\app\git\mingw64\bin
Git/CMD/SourceTree:
32 Bit: C:\Program Files\Git
64 Bit: C:\Program Files (x86)\Git
If your platform isn't listed, try and find git in either the Program Files or AppData folder for the respected program.
If whitelisting these executables does not solve your error, I suggest further network troubleshooting and contacting support on BitBucket Support or the respective support channel for the platform you are using.