A handful of hotels do offer shuttle service, it's best to call the hotel directly in advance to understand the situation. ALL airport hotels at ATL are on the Domestic side.
Uber/Lyft from the International terminal is quite a pleasant surprise, compared to the torture on the Domestic side. I've never had an issue. Uber drivers are not going to complain about the distance to the Domestic side. For example, International terminal to Atlanta Airport Marriott is 6.3 miles.