Mom has dementia. How do I manage her finances without financial POA?

You need to see an elder law attorney to apply for conservatorship or guardianship. Be certain first that you are capable, understand the task and are willing to do it as it is a lot of work. If you do not want to do it you should still see the attorney so that the state can take over guardianship and management of your Mom's care and her finances. Do know if the state takes it on you will have little to say.
You should not be paying for your Mothers care yourself; none of this will be compensated and what of your own care when you are aged?
See an elder law attorney today.
If your Mom has bills and you are going to take on guardianship or conservatorship you will need good files, so start them now. Each entity gets a file folder. Every penny into and out of Mom's accounts will have to be logged and accounted for. So notify all entities that your Mom is in care.
Does your Mom have a diagnosis of incompetency? If so take this proof with you to the attorney. If not, you need proof of same to be done, diagnosistic workup and so on.
By handling an account that is not yours online you may become accused of fraud. I hope you have kept all proof of withdrawals, and receipts of payments made though your Mom's account.
Visit the bank today. Explain what has been happening. Get the advice of the bank manager.
Meanwhile begin to research online "duties of conservatorship" in your state.
I wish you good luck.

Call an elder law attorney. He can advise you if she is still able to sign a POA. Without a POA you're helpless with the finances. Never mingle your funds with your mom's or you could end up owing her medical bills.

I would start with knowing with certainty what is going on with your mom's cognition. Just because she is "delusional and incoherent" doesn't mean it's from dementia: it could be from an untreated UTI (which is very common in elderly women and for which there often are no other physical symptoms in the elderly except change in behavior/confusion), vitamin deficiency, dehydration, diabetes, high blood pressure, over- or under-medicating of prescription meds, thyroid problems, tumor, etc. Once these have been discounted (or she's been treated for whatever issue is found) then she should have a cognitive evaluation. FYI "competency" is not necessarily discounted by short-term memory loss. It has more to do with comprehension. An certified elder law attorney can interview her to assess if she's competent. If she is, then if she's willing she can assign you as her DPoA. If not, I think conservatorship/guardianship is your only option BUT it costs money to pursue this through the courts (and your time). Maybe contact social services to see if you can get emergency guardianship, or have this discussion with them. Or discuss with the elder law attorney.

If you don't get guardianship, the county eventually will and then it will call all the shots and you won't have any access or insight into her medical or financial affairs.

I agree with others who advise to not co-mingle your funds with hers and please do not pay her bills with your credit cards. If she's late on paying bills don't worry about her credit rating -- at this point in life it won't matter for her at all.

I'm not sure I would talk to the bank yet -- they are on a hair-trigger when it comes to protecting clients against financial fraud. You will be suspect (as you already are). The bank would make you go through their own PoA protocol so IMO there's no point in talking to them. I'd talk to the attorney first.

I’m pretty much in the same position as you and it’s super frustrating. Mum lives with me and we go halves in expenses (well she’s always paid less rent). Mum has counted on me and my late brother to do a lot of her internet banking and other stuff even pre-dementia as she’s always been awful with technology and there’s a language barrier. Luckily when this once happened to Mum, we were able to solve it online. We would do it together as Mum needs prompting/pointing. There’s no way she could do it over phone. Ie if they asked her what her customer number/verification/passcode is,..she’d get confused what is meant by all the various terms. Having worked at a bank myself, prompting is not allowed. Therefore doing things online is much easier as we can go through the steps as slow as we need and I can talk her through things, help explain what is what. One thing I’d never do is put expenses through my own credit card and then pay the cc from her account. Although there are a few times I’ve directly transferred money into my account if I’ve for example paid for her groceries/incontinence products/chemist. That being said,.. Mum has through all her years transferred money to us kids (being a typical Mum). She still likes sending money to my brother who is in a care facility himself. Why? Coz his bloody state POA only gives him 20-30 euros a week for spending. So Mum has been supporting him for better quality of life. Ie now she wishes to buy him some shirts online and I believe she has all the right to do so being his mum! She still has her caring motherly instinct which brings her joy and I know it’s not out of character for her. Mum still wishes to dissolve his state POA but obviously that’s not happening. Quite frankly I hate this crap! Family is family! No one will ever look after my mums needs better. With my Mum she was too stubborn to do the POA earlier and now she can’t write anymore. She is able to say she wants me to look after her affairs and health with certainty BUT I can’t get anyone to do the competency test on her! I’m not sure if that’s “code word” for not competent and I’m just being given the run around? Is a person regarded as ‘not competent’ if they do need to be assessed and can’t walk into a lawyers clinic on their own? Is that how it works and I’m just not being told blunt?! I’m not sure!! However, I know for a fact she’s capable and competent enough to say she does not want the government involved and that she wants me (through her words AND her past experience with my brother). But this world always wants to get their grubby little hands on everything and interfere/control family matters. I’m actually really angry about my brothers situation (which probably shows) and do not want my Mum who has been battling his POA situation for years to be in the same situation. I don’t have anything to gain from my mum (no inheritance). I just want her remaining time here on earth to be as she planned / wishes. Ie if she wants to go to target and buy a silly soft toy! Why not! If it’s going to make her happy. If she wants to buy a summer dress (despite her not having many social outings), why not! She gets joy out of wearing it at home. Off course I make sure she’s not over spending and if she looks at something she already has, I remind her. The point is,.. she doesn’t have much left in this world... no friends, social events etc. in my opinion she is free to spend her money as she wishes! She has earned it and deserves it! I wish you all the very best of luck in sorting this out and I too hope to have things sorted with my Mum. I too am my moms full time carer and regardless of ups and downs (which I’ve expressed in some of my earlier posts), we’ve always been a tight knit family. Mum kind of brought us up that way. We’ve organised the 4 of us (3 kids and Mum) will eventually be in the same grave as well. 1 down (my late brother), 3 to go,..... We were far from a perfect ideal family but we’ve had each other’s back!