Cloud bursting temporarily expands the capacity of a cloud-based service hosted in a private data center by renting public data center capacity when the demand for capacity spikes. To determine the optimal resources of a business-critical web system deployed over private and public data centers, this paper presents a cloud bursting approach based on long-and short-term predictions of requests to the system. In a private data center, a dedicated pool of virtual machines (VMs) is assigned to the web system on the basis of one-week predictions. Moreover, in both private and public data centers, VMs are activated on the basis of one-hour predictions. We formulate a problem that includes the total cost and response time constraints and conduct numerical simulations. The results indicate that our approach is tolerant of prediction errors and only slightly dependent on the processing power of a single VM. Even if the website receives bursty requests and one-hour predictions include a mean absolute percentage error (MAPE) of 0.2, the total cost decreases to half the existing cost of provisioning in the private date center alone. At the same time, 95% of response time is kept below 0.15 s.