They are OK apart from the fact that you have singular / plural mismatch between hours and the verb. ...Hours have... ...Hours are... 'in a bit' is quite informal, so take care where you use it.

My shift has started. - Perfect. My shift is starting in a bit. - Perfect. My office hours is starting in a bit. - My office hours ARE starting in a bit. My office hours has started. - My office hours HAVE begun (started). If someone is talking about their office hours, it speaks more of when the office they manage is open to the public. Does that help?