How can I search bookmarks and history stored on mobile safari within iOS?
There is no interface for searching within Mobile Safari.

There is no secondary viewing options other than tapping and pawing through the history UI that mobile safari draws when you tap the book icon to the right of the navigation arrows at the top of the screen.

In the absence of a native solution, you can get at the history and bookmarks once you connect an iOS device to a computer.

On Mac OS, you can use a tool like PhoneView to archive all data from an iOS device, and this archive includes mobile Safari's web history and bookmarks so you can make fast work of searching the 8 days of device history once you have the data on your Mac.