Thanks for all the feedback. It is helpful. A few things:
1. On the idea of my mom going with me to the bank -- right now that is impossible.
2. Several years ago (with my mom's permission) I was going to set up online access for her for the bank.
I was my father's conservator for over six years (Alzheimer's) and that taught me a few things about these two concerns.
The most powerful legal form of delegated legal powers is a revocable living trust with her as a grantor/trustee and you as a contingency trustee. It's probably not an option for you now, but my spouse and I are setting that up for our elder years (with our daughter as contingency trustee).
You can petition your local probate court for guardian/conservator appointments. That's generally done when the elder is in a coma or dealing with dementia. It inserts the probate court into your caregiver life as a benevolent overseer of many administrative reports and an occasional judge's order. It's no fun but sometimes it's the only legal option (especially when there's no RLT).
Perhaps your most practical option right now is a durable POA. Those are not always accepted by financial institutions, or they may insist on having yet another durable POA executed on their own custom form. However I encountered plenty of disrespect as a conservator, too, so a durable POA might be the best alternative.
Regular ol' POAs are technically (and legally) invalidated upon impaired cognition or death. They can also be revoked at any time, which can be a problem if elder vultures prey on your mother and ask for a POA as her special friend.
When Dad entered a care facility, we felt very lucky that he did not own real estate. I can't offer any help with that issue, although a durable POA may be the answer.
If your mother agrees (and while she's still healthy enough), I'd set up everything to be done online. (I agree that her bank is not helping, and you could ask the bank what "Yes" would look like so that you can lawyer up if necessary.) You don't always have to switch the places where she currently deposits her Social Security and other payments, but you'd certainly want to set up automatic transfers from those accounts to other accounts which you either access online or where you're a joint owner.
My father's pension & SS were deposited in a local bank which was hostile to me from the day Dad entered a care facility until he passed away... and then for several months afterward. (We're still disputing Dad's account balance with them, but it's only $1.26.) However it was still less hassle to deal with this bank than to switch a SS deposit and a pension deposit, even with a conservator's appointment. After the first month with that bank I just started transferring out all the deposits every month (leaving behind $100). On the day Dad died I transferred out another $99 before notifying the bank of Dad's death.
That last paragraph involves techniques which may be technically illegal (even felonious). However Dad's business got done, I maintained records of my fiduciary behavior, and the bank officially ignored everything as long as they could.
You mentioned "signing the checks". I initially came under the gimlet eye of Dad's bank due to my helpful assistance of filling out his utility bills for his signature. (It kept him occupied while he was in the hospital.) This "filling out the checks" practice is apparently a classic sign of elder abuse. As soon as Dad's bank saw the checks in my handwriting (even with Dad's actual signature) they locked me out of his account. It took us nine months (and a probate court's conservator appointment) to restore access.
You can sign up for online accounts with Social Security and Medicare. (Or just update the mailing address and continue to do business with paper.) Social Security will verify ID with a credit-reporting agency, so unfreeze her credit records before signing up for online accounts. I also did fine with SS on the phone for changes of address & phone number. They seem to know the difference between caregivers and elder abuse.
You may want to freeze your mother's credit now, and perhaps let her credit cards expire. I belatedly remembered to cash in Dad's rewards points.
When you file your mother's tax returns, the IRS and the state may want you to verify her online ID with a driver's license or state ID card. (It depends on whether she's been a prior victim of tax ID theft.) You can also sign her up now for online taxpayer verification or a PIN.
Your mother should verify that all of her retirement accounts (especially IRAs) have designated beneficiaries. It's also very helpful to designate "payable on death" or "transfer on death" to every one of her other accounts. This greatly simplifies probate (or avoids it entirely). It also lets you request disbursement via an affidavit instead of having a probate court issue you a letter of appointment as a personal representative. I was able to ask Navy Federal Credit Union, USAA, and Fidelity to disburse large sums with affidavits because he had POD/TOD on those accounts. The lack of POD/TOD on Dad's checking account is why Dad's old bank and I are still disputing $1.26.
3. I am very reluctant to add myself to her bank account for two reasons. One - I worry that would create some risk for her. That is, what if I was sued or had some liability and someone tried to collect the money from that account because my name was on it? I have no debts and pay my bills but someone could wrongfully try to collect something. Second - If my mother were to need nursing home care and lived long enough she could exceed her assets and need Medicaid. Would it muddy the waters in her qualifying if I was on the account and writing checks (even if all of them were for her benefit)?
If you do open a joint account with your mother, you could make it separate from all of her other accounts and transfer money to it. Limit its balance to just enough to pay the monthly bills. That minimizes the liability risk. Medicaid won't care, although they'll look back through five years of records for any large fund transfers (like gifting) to make sure no assets were being illegally hidden from the Medicaid requirements.
When I was Dad's conservator, I continued his history of gifting my brother and me. (I had to get the probate court's approval, and they didn't care.) It helped my brother (who occasionally asked to borrow money from Dad's assets). It gave me a "Dad emergency fund" to tap if I had problems with any of his financial accounts. It was also my backup care fund if he went on Medicaid, so I had projected his gifting to stop at least five years before his assets were depleted.
FWIW, I plan to go to be bank probably Monday and talk to them since that is the main one that needs to be done. I will go to the branch that she has banked at for over 50 years since I want to check the safety deposit box (I am on her box and have been for over 40 years).
I've read many stories of caregivers who, when their elder dies, quietly visit the bank and empty the safe deposit box before formally notifying the bank of the death of the elder. Some of them simply transferred the contents to a box at a different bank. The banks seem to ignore this behavior if no other heirs complain.
This may not be a concern for you since you're on the box, but you might want to reverify the bank's policy for the death of a box holder.
You seem to be doing just fine, but I found it tremendously helpful to hire a geriatric care manager in Dad's local community for a couple hours of advice & assistance. They know exactly how to tap into community & state resources (especially Medicaid) to make life easier for both caregivers & elders. If your mother's a military vet (or a surviving spouse of a military vet) then a GCM can help figure out any veteran's benefits.