I almost have this polished, just one little piece that may be beyond what my pea brain can handle. The short of it is that from the affected contact you need to send an e-mail with tokens. (I've put this into a template.) In the body of the e-mail put a link similar to this:
https://yoursite.com/civicrm/?page=CiviCRM&q=civicrm/contribute/updatebilling&reset=1&crid=XX&{contact.checksum}&cid={contact.contact_id}&context=dashboard
You need to replace the crid=XX with the correct crid for that failed transaction. The only way I've found to get that crid from the front end is through a few steps.
1. Open up the contact of the failed contribution.
2. Click on the "Actions" button, then Right Click on the "Contact Dashboard" and choose "Open in new Tab." This will open up the dashboard in a separate tab, as you'll need the first page later and can't easily get back to it.
3. On the Contact Dashboard page, you'll find a "Recurring Contributions" line. Click the "more" button, then Right Click on the "Change Billing Details" and choose "Open in new Tab." This will open up the "Billing Details" in a new tab. In the address bar, you'll find the "crid=" value buried in the string.
Moving forward, I'm hoping that someone with more skills than I can figure out how to add this crid as a token, and then be able to search for failed contributions and send the template e-mail to multiple contacts at once. To go even a step further, being able to automate this once a failed transaction happens, the system automatically sends out this notice.