ci: use GitHub App to make PRs (#490)

Signed-off-by: Henry Schreiner <henryschreineriii@gmail.com>

.github/workflows/bump.yml

@@ -13,6 +13,11 @@ jobs:
     name: Bump versions
     runs-on: ubuntu-latest
     steps:
+      - uses: actions/create-github-app-token@v1
+        id: generate-token
+        with:
+          app-id: ${{ secrets.APP_ID }}
+          private-key: ${{ secrets.APP_PRIVATE_KEY }}
       - uses: actions/checkout@v4
       - run: pipx run nox -s pc_bump
         env:
@@ -25,5 +30,6 @@ jobs:
           body: |
             Update the versions mentioned in the docs pages.
 
-            PR generated by "Update dependencies" [workflow](https://github.com/${{github.repository}}/actions/runs/${{github.run_id}}). Close and reopen to trigger ci.
+            PR generated by "Update dependencies" [workflow](https://github.com/${{github.repository}}/actions/runs/${{github.run_id}}).
+          token: ${{ steps.generate-token.outputs.token }}
           delete-branch: true