Go to the top right corner, click the dropdown arrow beside your profile picture, and select your personal profile. This way you know you are interacting as your personal profile for now.

Click the Join Group button. This will either be near the top of the page, or in the lefthand panel.

Your request to join that group is now pending, so now we need to switch to interacting as your business page to approve that request

From the top corner again, click the dropdown arrow beside your profile picture. This time though, select your Business Page profile.

From the lefthand panel, select Member Requests.

(You may need to click the Manage tab in that panel first, to see that Member Requests option.)

Find your personal profile in the list given, and click Approve.

Click the Member tab at the top of the page.
(You may need to click Community Home on the left first, to see the Member tab)

Find your personal profile on that list, and click the 3-dot icon beside your name. Select Add as Admin, and confirm that you want to send an invite.

Almost there! Now, we need to swap back to our personal profile one more time, up in the top right corner of the page.

Now that you're interacting as your personal profile, there will be a banner either at the top of the page or in the lefthand panel, asking you to accept the invitation to become an admin. You may have also received a Facebook notification, with that invitation. Make sure to click Accept in any of those locations.

Both your personal profile and business page should now both be admins of that group!