Right now I am using the popover controller to function as a dropdown menu on buttons. However, the overhead of this approach is annoying. Creating a new component and module, adding the component to the entry components, importing the module, etc etc…
Dropdowns are quite simple components, you can handle them with display style property. For example make a simple div element and put your stuff in it. Manage div presence with display:block; and display:none;.
How I do it is to use ion-card component, ion-card-header is always visible and clicking on it triggers ion-card-content display property. You can also add some easing animation on it (in that case you should consider using max-height property instead of display)