How do I connect Splitwise to my bank account?
You can't – not yet, anyway.
Splitwise doesn't actually handle any real money, and it can't automatically pay your bills for you – Splitwise just helps you keep track of how much you owe to other people. When you add an expense on Splitwise, it's like a digital IOU. When you add a payment to another person to settle that IOU, it's up to you to make sure that the other person receives the money, either as cash, via PayPal, or by other means.