It's a bit unclear what you want. What is a bank card?
Master and Visa are credit cards and credit cards will only be issued if you can proof you have a steady income.
My Chinese debit cards (BOC and ICBC) are both UnionPay enabled which means they can be used abroad to get local cash out of the wall.
The basic difference is that with a credit card you basically borrow money from a bank thus the name credit card and they want to be sure you can pay that back. A debit card only allows you to withdraw money you actually deposited at the bank. This is much more secure for banks and therefor it is quite easy to get a debit card. But make sure foreign use of UnionPay is enabled.
Since a debit card is not a credit card it can’t be used for things like renting a vehicle or certain/most (Outside China) internet purchases.