I want to ask a person what time should I start to work.
What is the regular office hour?
OR
What are the regular office hours?
Unless the period of work in question is a specific single hour (unlikely), the correct version is your second one.
Alternatives might be:
What are your business hours?
What are your opening and closing times? (If it's a retail business)
What hours am I expected to work?
In academia, an office hour is an appointed time when a professor is available to meet with students who might have questions.
To avoid confusion, you might want to use a different expression, like one of these:
Note: Those questions are designed to give both a start time and an end time for your work day. If you are primarily interested in what time you start your work day, you can use one of these: