How does the path cross the street?
Generally, unless marked up all over the place with signs, crosswalks, etc... the car has the right of way. It is another reason bike paths stink--- they often cross roads in the middle of nowhere, where cars are not expecting cross traffic- like in the middle of a block in a residential neighborhood. It sounds like in your case, the general signage indicates that bikes must yield. The best you can probably hope for is to have a sign installed at the intersection in question.