```python
from collections import deque
from typing import Dict, Optional

class JobQueue:
    def __init__(self):
        self._queue: deque = deque()
        self._results: Dict[str, dict] = {}

    def add_job(self, job_id: str, data: dict) -> str:
        self._queue.append((job_id, data))
        return job_id

    def get_result(self, job_id: str) -> dict | None:
        return self._results.get(job_id, None)

    def process(self) -> Optional[str]:
        if not self._queue:
            return None
        job_id, data = self._queue.popleft()
        result = {"status": "completed", "data": data}
        self._results[job_id] = result
        return job_id
```