Bloated transaction log and .bak backup size confusion
How is a 365 .bak file restoring both a 369MB .mdf file and a 29.7GB 
  .ldf file?


It's not restoring the data from the log file, or backing it up, it's just creating it with the same size as it was when backed up.  Check the free space and it should be 99% free.


  Any suggestions on what to do regarding the recovery model and bloated
  .ldf file? We are only concerned about doing backups once nightly - we
  don't need to do differential backups at this time - but it's
  something I will tackle later.


If you are only worried about doing backups once a night then change the recovery model to simple.  If you leave it in full you will need to perform log backups as well.  Once you switch the recovery model or start performing log backups you could do a one time shrink to get back the space.