That's right, there is no bike lane there. I ride my bike down that road every day, sometimes multiple times a day. I am very cautious while riding whether there is a bike/pedestrian lane or not. It is the drivers who need to pay more attention to what is going on around them. If a cyclist is riding in the lane in front of your car, then HE, the Cyclist, has the right of way.
Please pay attention to what you are doing and share the road. It is a public road, not just for cars.