Childminding isn't a Pay As You Go service, generally. Instead it is like most contracted services (for childcare sector, nurseries and nannies are both usually contracted services), so the customer agrees a contract with the service provider. Under the terms of that contract, there may be occasions when the service provider charges a fee, even when they don't provide the service to the customer - bank holidays, training days etc.
It is common practice to charge for bank holidays, as a nanny I get paid for bank holidays but I don't work them, if you took your child to a nursery the nursery would I expect charge you for bank holidays yet they would not be open.
Your employer in turn will most likely be paying you on bank holidays, and if you are self-employed you should be factoring in holiday pay into the fees you charge your clients.