My ears get bored on busses so I consume a lot of audiobooks. Dropbox is my main backup solution and it contains the majority of my collection. I wanted an easy way to consume those audiobooks on my Android device. This is what I did;
Install Smart AudioBook Player, it's free, has no ads, and is available in the Play Store
Create an Audiobooks directory in Dropbox and store your books in separate subdirectories
Make the directory of the book or books you are currently listening to Available Offline. You can also optionally make the whole Audiobooks directory Available Offline however that may take up a lot of space on your device
In the library settings of Smart AudioBook Player, select the Dropbox data directory as the root folder. The location may be different on your device/version of Android. On my device it was /storage/emulated/0/Android/data/com.dropbox.android/files/[user_id]/scratch/Audiobooks. Checkout this stackexchange post for hints as to where it lives on your particular device
Hit refresh in Smart AudioBook Players Library. The books that are currently stored offline should appear
Select your book...
And enjoy your trip with Dropbox hosted Audiobooks on your Android Device!