The per-hour limits apply to links created through the Bitly API. By default, the hourly limit is set to 10,000 links/hour for an Enterprise account and 1,000 links/hour for lower subscription plans.
The per-minute limit is 1/10th of the hourly limit, and it resets every minute. To increase the per-minute limit, you increase the per-hour limit. For example, an hourly limit of 10k calls translates to a per-minute limit of 1,000 calls.
If you'd like to increase your limits, please contact our sales team or reach out to your Account Manager if you have a managed account.