You may want to try
Aldiko.
Aldiko can be registered with Adobe to read DRM'ed library books, is much faster than Overdrive's app and is also more feature-rich. The speed of page turns alone makes Aldiko worth switching to.
There is a free version and a premium for $2.99 and the premium is, from what I understand, mainly a donation for development. I never noticed ads when using the free version and the $2.99 seems worth it for such a useful app.
There is also another reading app or two that can handle Adobe DRM, but I don't remember what it/they is/are.