I think we might need to apply for guardianship but I can't afford it. What can we do?

AFTER you win guardianship (and with a Mom with dementia and no one else wanting guardianship, you will) you can reimburse yourself carefully out of the account. (If you do not win guardianship you do not get reimbursed; that would be if your Mom was fighting you on this issue).
HOWEVER know that you actually WANT this. You now will be in charge of all decisions and all accounts and you will be working hard to keep all of this straight as POA for all accounts. You need to know how to keep good files, good books, and etc. You may prefer a court appointed guardian for your Mother. You may want to speak with a social worker about how to proceed. Someone in Estate Management.
Or pay at least for that 400.00 hour of time to ask questions of an Elder Law Attorney. Try to get a referral to a good and decent one and make it clear you are paying an hour to ask about OPTIONS going forward; make it clear that you do not have a lot of funds; some work with senior centers and actually donate hours and time.
Gather all the info you can. Go to Senior Centers if in your area. I hope others on forum have some ideas of where you can seek info.
Geaton is correct that the State may take guardianship. If they will I say LET THEM. It is hard work. They know how to do it, and will let you know what they need. Talk to the facility about the possiblity of that. Try not to get too crazy and look on this, the two of you, as information gathering time. An hour of time with the Elder Law guy will likely take 200.00 of the purses of each of you, but may give good info. Have the questions right there.
How much would it cost to get guardianship on a dementia Mom (give her details as you know them)
What would happen if we allow the State to take guardianship?
and whatever other questions you have.
Good luck. Let us know what you learn.

I went through guardianship conservator process for my parents. It cost over $3000 and took almost 4 months and this was a simple uncontested case. I was having the same problem with a bank not releasing funds even though I had a POA.

The alternative may be to contact your county/state APS office or other seniors agency to get direction on having her made a ward of the state. A guardian would be appointed by a judge. The administration at the nursing home would probably be able to advise you on how to go about this. They want to keep the rooms filled. It would be in their interest to free up the money from this bank.

If she did not declare POA before she became incompetent, she cannot do so now. And you cannot try to get her to make any legal decisions. The bank is right not to allow it. Go to elder law attorney for advice. If you want to let the state take guardianship, then understand you have no input at all. If you are okay with that, take that route. But the money spent for an attorney consult is well spent and you can use her funds for that.

DH has POA for both his parents and is the succession trustee if they are unable, and we still had neuropsych evaluations done on them and that doctor wrote a letter to say each of them is not competent to make any financial and medical decisions. Which is true. It was a lot of hoops to jump thru even with the POA. Their POA was done 20 years ago so we had banks telling us the POA was old, which did not make it invalid but we still had to prove a bunch of stuff. If there are symptoms, Medicare does pay for neuropsych evaluation if family doctor writes order.

As to cost...You do not pay the cost of Guardianship the Ward will pay (or the Wards account will be charged)
Any cost that comes out of your pocket can be reimbursed to you from her account.
Yes it can get expensive. It can be frustrating. There is a lot of paperwork.
I agree with BarbBrooklyn is there a way to get your mom to the bank? Is it possible to set up a way that the one account will automatically transfer $XXX. over to the other account monthly?

Call Legal Aide in your area.

Please ask the social worker at the ALF to help u find an attorney that's less money. Maybe even pro bono, (is that spelled right?) Sometimes senior services, in ur county, can help pay, (or other groups). Good luck:)

Your mom only pays the fees if she can afford to pay them and in some states, you have to pay out of your own pocket and then be reimbursed. If neither of you can afford to pay then there may be financial assistance through the courts.

Don’t discount the fact that many lawyers as well as Elder Law Attys offer free consultations. Might depend on how large of a city/area you live in. In Southern California I was able to access Free Consultations from two different Elder Law Attorneys Office’s, and both were very helpful too, also I called Legal Aide and received even more help. Bottom line is you have to start dialing for help, and don’t stop until you get satisfaction. There’s no “how to” books out there that I have found. Just keep reaching out everywhere, and anywhere. Eventually you will find the assistance you need.

Talk to an elder lawyer who can outline all the options available where you live.

So good to hear that your sister is one of the helpful siblings! So many are not, and some are even detrimental!

Often EC attorneys will give you a first consult for free (likely 1/2 hour or so) where you can ask a lot of questions and find out what they think the best/worst case of costs would be. I would find 2-3 at least, and have a list of questions prepared, and take notes during each consult.

The assets of the person who needs guardianship are generally used to cover these costs. Given that you cannot access those assets at this time, you would have to add that to the list of queries for the attorneys.
**IF she has enough, it could go one of two ways - they could allow most of it to wait for appointment when you would have access OR allow you to make payments and get reimbursed after appointment. Keep VERY good records/receipts of anything you spend of your own money.
**IF she doesn't have assets for this, then add to your list of questions whether there are any low cost options to help you out.

I do know from having dealt with EC attorney for dad (mom was still capable, but difficult to work with!) that the process CAN be sped up in cases of real need. You should ask about this too, if there is a serious need to get those funds moving!

In a response to someone else's comment, I posted this:

https://www.lawyers.com/ask-a-lawyer/family-law/how-much-does-guardianship-cost-1615061.html

It is OLD, from 2013, but you can see from the legal responses to the query that the costs can vary a lot. Another note from that post is that what you need for accessing finances is Conservatorship. Guardianship is generally for overseeing the person and their care. Conservatorship is for managing finances, etc. In your case it would likely be best to have both. This will increase the cost as there would be additional filing fees and legal aid, but again, ask the attorneys during your consults.

Handing over one or both of these to the state takes you/family out of the picture. You have no say in where they live, how their remaining assets are used, medical care, nothing. Personally I wouldn't do that. If there were limited/no funds and no love for/from the person (there are "distant" parents/other LOs, or even belligerent ones), then perhaps, but in your case y'all care for your mom!