ok listen pretty much everyone is suggesting the same thing, open a local IDR bank account AND a foreign currency one, no offence but I don't know why you keep questioning us. You will need a local bank account at some point even if its just a place to keep rupiah, and a local debit / atm / credit card is always useful
I suggest BCA for IDR and then go to HSBC and open a USD and or EUR account and even IDR if you want. It costs the same (nothing) and the monthly fee is absolute peanuts.
Take your cash USD to the money changer, dump those IDR into your local accounts, and put some into the USD account or put some of the USD into HSBC before you convert the rest, up to you
But just open a local IDR and HSBC for forex. Simple