Some users may not be able to accept invitations to private blogs unless they are already signed into Blogger. The problem is frequently accompanied by a bX-b0uqh3 error message.
We hope to have this issue resolved shortly, but in the meantime here's a workaround:
1.) Copy the sign-in link from the invitation email.
2.) Navigate to Blogger.com and sign in.
3.) Paste the original sign-in link into your browser's address bar, where you should then be given access to the private blog.