This is not difficult. You first make a new Google account, to own the Google+ Page.
Everything that follows is normal Blogger blog management. Don't overlook the details of blog management, though.
The process of making a Google+ Page a blog owner is not so complicated - but it has to be done, carefully.
- Add a password, to the Page.
- Setup a GMail email address, for the Page.
- Make the new Google account a blog owner.
- Add blog and page relationships.
- Add blog content, using the new(?) Google account.
Add a password, to the Page.
See Google My Business Help: Set up a password for your Google+ page, for this step.
Note: In some cases, you may have been previously instructed to setup a Google account to manage the Page. If you already have a business Profile setup, skip straight to Step #3, and make the existing Google business account a blog owner.
Setup a GMail email address, for the Page.
Setup a new GMail email address, while logged in to your new account - if this has not already been done.
Make the new Google account a blog owner.
Once you have a new Google account with a unique email address, transfer control of the blog, to a Blogger account based on the new Google account. And make sure that your new Blogger account uses a Google+ profile.
If you want, put the blog under team ownership - though as always, know the risks of team ownership.
Add relationships between the blog, the Google account, and the Google+ page.
Add appropriate links, from the blog to the page, and back. And add the appropriate accessories to the blog - the Google+ badge, or maybe the +1 Button, are good, to start.
Then, add automatic sharing of posts - and maybe Google+ hosted comments. If you add the latter, be aware of one known peculiarity of Blogger and Google+.
Add blog content - while using the new Google account.
Finally, login to Blogger, using the new Google account. Then, start publishing content - and add value to your blog.
Anything you post to the blog, using your current Blogger account, will still be shared to Google+ under your personal profile. You need to be actually using the new account, to share to the Google+ page.
Be aware of possible complications, depending upon how you publish and share.
Sharing to a Google+ page is most reliable when you use the "Share" menu link, in the dashboard Posts page. Automatic sharing, and scheduled posting, may or may not produce the same results.