Breakfast near Bakersfield amtrak station
I am assuming that you want something within walking distance and that you have no vehicle.
There isn't much in the way of restaurants offering near the train station. That area is a mix of residential, city government buildings and some businesses.
I don't recommend the Hill House in the Best Western which is across the street from the station. I've had dinners there and it wasn't very good.
There is a Holiday Inn Select (801 Truxtun Ave) about a block or so west of the station that serves better food (but it is still hotel food). I've had lunch there and it was decent. I am assuming they serve breakfast, as well. You should call before heading there to verify that they serve breakfast.
If you had a vehicle, I'd say go to the 24th Street Cafe which is at 24th and K Street, not really walking distance.