I would say banks can help with this; but bank trust departments have changed over the years. Out here, they're much like a private banking relationship, with high touch and high fees. Used to be they would administer bills, help with other financial situations for a monthly fee, but I think it's more complicated today (a requirement that you use them as FA in an AUM arrangement, plus fees for the day to day expenses - and for only as long as you have enough under management to make it worthwhile).
More to your question, in CA, we have a group of licensed professionals called "Private Fiduciaries", with typical professional licensing and certifications. (I'm not sure if this is a CA title or a common title used nationwide).
At the most simple level, these fiduciaries/firms operate on an hourly basis and can be tasked with paying bills, coordinating with accountants, lawyers, and even doctors if needed (although you need to sign HIPPA and POA type documents for health care, I expect). They're principally set up to help those who can't take care of these things for themselves, rather than as a convenience; so I expect they could be an answer to your question.
It's worth knowing that at the most complex, they can handle everything, even become a Successor Trustee to a Trust (although more legal documents/POAs needed, as well as listing them in your Trust documents, of course).
Obviously, for any purpose, you'd want to check them out, interview them, etc... A referral from another trusted professional on your team (lawyer, accountant, physician) could be a good place to start.