Car starting on its own?

If you mean you hit the doorbell and the engine starts, it sounds like they are using the same frequencies. Nothing to really fix if that is the case as there isn't really anything you can do unless the doorbell or remote start can have different frequencies selected. The first thing I would do is to verify that hitting the doorbell starts it every time. If not, then it's possible something else is doing the same thing. So first will be to look and see if the remote start is a factory unit. If not, you might be able to change it out for one that doesn't have that problem. If it's a factory unit then see if the doorbell can have its frequency changed.