Can you legally hang a bow from the window in your truck?

Sure.

Bows, other than prohibited crossbows (those which can be fired one handed and less than 500mm in length) do not require any type of license or permit to possess in Canada. There is no law which prevents you from having one in your vehicle -- other than you can't take a weapon onto private property within the permission of the owner or take a weapon to a public gathering. In Alberta, most private places aren't going to care if you have bow in a parking lot provided it remains in the vehicle. If they do, you have to leave. Few parking lots would be considered a public gathering -- baring a school, large protest, or something.

It might cause law enforcement to ask questions if brought to certain areas -- say a park where they might think you are illegally hunting. It is also generally stupid as bows are typically expensive and might encourage someone to break into your vehicle to steal the bow.

In Texas bow but no arrows

Yes.