I have made quivers out of cherrybark, birchbark and elmbark. Aspen I haven't tried.
Not many types of bark after drying have the properties that they become / remain leathery or somewhat flexible.
Birch or cherry are used by a wide variety of cultures for containers / vessels, because they are very water resistant. In elm bark, it is the cambium that becomes very leathery - but elm bark is not very water resistant (see Ainu quivers made from elm bark with a cherry bark wrapping).
I haven't tried poplar or aspen, though poplar was traditionally used for large wooden bowls (light wood, easy to work with, and relatively water resistant - but that's for the wood, not the bark).
P.S. I know some guys, who have made some side - and back quivers from poplar bark. They harvested the bark in spring and let it dry around a small tube.