"...her being left with a loan or credit card bill for all the fees."
If there are more debts than assets then these debts are paid off in a set order.
From what you have said, it is very unlikely that Bethany will end up out of pocket.
If an estate is insolvent (ie more debts than assets) then the order that the debts must be paid off is as follows:
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Secured loans. Eg a mortgage or other loan secured on the property. These get paid off first. As long as Bethany's mum wasn't in negative equity (ie her mortgage was more than the value of her home) then you move on the next category.
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Reasonable funeral and administration expenses. This includes things like probate fees, court fees, solicitor fees etc.
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Preferential debts. If Sarah employed somebody and owed them wages or owed tax to HMRC etc then that comes next.
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The capital value of any unsecured loans.
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Any interest due on unsecured loans.
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Any informal loans, eg between family members.
So, as long as Sarah was not in negative equity, so any mortgage or secured loan was not greater than the value of the house then Bethany will be able to use the money to pay for the funeral and probate costs and court costs etc before giving a single penny to any unsecured creditor.
"... or finding more debts, ... Is there any way we could run a credit check?
If there is a real possibility of there being more debts that you don't know about then one thing that is often advised for executors to do is to place a Deceased Estate's Notice in the newspaper.
You have to place it in The Gazette (see link below) and also a newspaper local to where the property is.
It gives Sarah's name, address, date of birth, date of death and occupation if any. It also states that Bethany is the executor.
If you are in England or Wales then any creditors only have two months and one day to come forward and make a claim against the estate.
After that you don't have to worry about any unsecured creditors (eg credit cards etc).
Again, the cost of doing this comes out of the estate before any money is given to any unsecured creditors.
[EDIT]
Forgot to include the link!
https://www.thegazette.co.uk/all-notices/content/103403