I've looked through the available websites that had information about Hotel Billing Software, but none provided the details regarding these apps and the possibility of them working together.
Because of that, I can't really say if BusyWin will work with Hotel Billing Software. Based on my opinion, I can say that QuickBooks might be a better alternative that can be integrated with Hotel Billing Software.
Send an inquiry to the developers using the following link: https://help.quickbooks.intuit.com/en_US/contact