You are covering the bills out of your own pocket, and the bank keeps asking for a form. Adding your name to Mom's account looks like the simple fix. Sometimes it is. But the form is a decision about who can move money, and that decision should be checked before you sign, not after the first bill goes sideways.
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Ask the bank what access the added name gets
Banks use different words for this. Some add a joint owner. Some add a signer or a person who can write checks but does not own the money. Ask the bank to explain, in plain words and in writing, what the added name can do. Can you withdraw everything? Can you close the account? Can you change the address or the phone number? Does the bank treat the money as Mom's or as shared? Get the answers before you sign and keep a copy of what they told you.
Check what the account does for Mom
Look at every deposit and every automatic payment that runs through the account. Benefit payments, pension deposits and rent from a tenant can behave differently once a second name is on the account. Ask the bank whether anything about those deposits changes, and ask the agency or payer that sends them whether an added name affects how they pay. Write the answers down next to the bill list.
Decide what the money is for
Write one line that says what the account is for. Mom's housing, her utilities, her medical bills, her groceries. Then write one line that says what it is not for. If the account is also where you front the bills for your own household, or where a sibling pulls cash for a car, say so. The line is the boundary. Without it, every withdrawal becomes a question nobody can answer later.
Tell the other siblings
This is the step families skip. Tell each sibling, in writing, that you have been added to the account and what your access is. Do not wait to be asked. A sibling who learns about the account from a statement will read it as a secret, even if it was a bank form and nothing else.
Check with a professional before you sign anything that changes ownership
Adding a name to a bank account can have effects on estate planning, on benefits and on taxes that depend on the details. A Missouri estate or elder law attorney can read the paper with you before you sign. The Missouri Bar and the Consumer Financial Protection Bureau both publish public guidance on what to ask. Start there and bring your list of questions. The paper is the bank's, but the decision is yours, and you should be able to explain it to your siblings in one minute.