Luiz I have traveled to the US with my bunq cards a few times. My experience: when you turn on the unsafe payment method by magstrip then 90% of the times you should be okay. Some petrol stations gave me a hard time.
In general I would not use a debit card for car rentals and check in at hotels. Any deposit will be deducted from your account (most hotels even have warning signs about this) and the return might take days or weeks.
For traveling a decent credit or charge card is in my humble opinion a necessity. Get yourself a VISA and send it back after the trip, you should only be paying for two months then.