I am going to strongly recommend you download and purchase "Bookmobile." It is hands-down the best audiobook app out there.
After iOS 7 came out and slapped my audiobook experience upside the head, I tried a few different ones. When Bookmobile first came out, it wasn't great, but the developer issues regular updates. It's now largely bug-free and works exceptionally well. At first, I didn't love the UI but it's really grown on me.
Some highlights:
Viewable/selectable chapters
Supports Audible downloads as well as m4b; I haven't tried an iTunes purchased audiobook
Tap the timestamp to swap between how much time is left in the chapter to how much is left in the book
10 different speeds (you can speed up the audiobook slightly to listen to it faster without it sounding like Alvin and the Chipmunks)
Dropbox support (and several other ways to add audiobooks)
Edit audiobooks within the app (titles, authors, etc)
Customizable skip-forward/back buttons (this is a real gem; also, tap to change from skipping back by seconds to skipping by minutes)
I don't know or work for the developer, I just know I seriously can't imagine listening to audiobooks with the native app ever again. I've attached two screenshots.