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

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

    def add_job(self, job_id: str, data: dict) -> str:
        self._queue.append(job_id)
        self._jobs[job_id] = data
        self._results[job_id] = None
        return job_id

    def process(self) -> Optional[str]:
        if not self._queue:
            return None
        job_id = self._queue.popleft()
        if job_id in self._jobs:
            # Simulate job processing
            self._results[job_id] = {"status": "completed", "data": self._jobs[job_id]}
            return job_id
        return None

    def get_result(self, job_id: str) -> Optional[dict]:
        if job_id in self._results:
            return self._results[job_id]
        return None
```