Trying the Bing Maps drawing tools, looks like you have to click each point of your shape, it doesn't draw on mouse down/drag.
If you are open to other map platforms, Azure Maps drawing tools provide a lot more control over this and the default uses a hybrid approach where you can click each point or mouse down/drag. https://azuremapscodesamples.azurewebsites.net/?sample=Drawing%20manager%20options