When Katy wants to pay ₿3 to Billie, Katy just sends a key (via email or some API) to Billie which enables Billie to withdraw ₿3 from the account of Katy. But Billie does not do that. Billie just keeps that message like you keep your login to your bank account.
When Katy wants to pay another ₿5 to Billie, Katy sends a key to Billie which enables Billie to withdraw ₿8 from the account of Katy.
Now Katy paid Billie ₿8 in two transactions. All via email, letter, telephone or - most likely - API. Nothing at all happened on the Bitcoin network.