When your customer has a Bill.com account, you'll get invited by them so they can pay you digitally. If you're able to create your own account, you'll receive an email notification showing the summary of the bills paid by the customer.
Although, if you're unable to receive any notifications, I suggest reaching out to Bill.com's customer care support. They'll help you trace the payment.
The Community is open if you have other concerns. Don't hesitate to reach out to us. Take care!