No matter what browser or PC I try to log in with, this same error persists. I can log in fine to atlassian.com and I can use this same account to post this question, but I can't log in to Bitbucket.
You may run into this issue when you use specific browsers or add-ons that hide the referer header for id.atlassian.com and other Atlassian sites. Check for these and then try logging in again.