Bitrise Checks works only on Github, not on Github Enterprise. For Github Enterprise, you can use the Github Status Step.
The Step uses https://developer.github.com/v3/repos/statuses/ endpoints.
When a status is reported for a PR, it will show up first on Github surface in the Repository settings tab, under Branches > Branch protection rules.
Create a new rule. This should bring up the rule edit view:
Select the report in the bottom to make it show up on the PR view.
Statuses are always set for a commit hash. Each time a PR is created, it will belong to the commit hash itself. Each commit will have its own commit hash.
This is how it will look like for the PRs:
And this is how it will look for commits: