Hi Bonnie!
First, welcome to the community! 
You currently have to use Python 2.7 for both the JIRA bridge and the Shotgun event daemon. We haven’t ported these components yet to Python 3.
The error you have seen during the import of shotgun_api3 in the JIRA bridge when using Python 3.7 is due to the fact that the JIRA bridge’s requirements.txt file has pinned the version of the Python API to 3.0.39, which wasn’t Python 3 compliant.
We’re still porting our code to Python 3. Our current focus is on the Toolkit components. JIRA Bridge and Event Daemon are going to be ported at the tail end of the port. The reason Toolkit is prioritized over these two components is that the bridge and the daemon run with a version of Python that our clients have complete control over.
On the other hand, for software like Maya and Nuke, our clients are at the mercy of whatever versions of Python the software vendors decides to ship with. We do not want clients to be blocked from upgrading to a more recent version of a product because we do not support Python 3. It’s looking like most of the software vendors are going to be shipping support for both Python 2 and 3 this year, but there’s no guarantee how long they will. Plus, certain DCCs, like Blender, only support Python 3.
Cheers,
JF