Cloud bursting temporarily expands the capacity of cloud-based service hosted in a private data center by renting public data center capacity when the demand for capacity spikes. This paper presents a cloud bursting approach based on long- and short-term predictions of requests to a business-critical web system to determine the optimal resources of the system deployed over private and public data centers. 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 formulated a problem that includes the total cost and response time constraints and conducted numerical simulations. The results indicate that our approach is tolerant of prediction errors. 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 a half the current cost while 95% of response time is kept below 0.15 s.