This is related to, but not the same as, https://community.atlassian.com/t5/Bitbucket-questions/How-to-accept-invitation-to-shared-repo-on-existing-account/qaq-p/696937
There doesn't seem to be a way to accept an invitation to a Bitbucket repo without clicking on a link in an email; in particular, I'm logged into my account and don't see any way to view invitations made to me. It's slow and clunky to go through my email. Much more importantly, links in emails are a security issue. Surely a product aimed at developers should expect them to be savvy enough to have a problem with this?