On the Keyboard issue....
Personally I use Swiftkey on my Nexus 7 and for the 90% of the time I am typing it works. It splits the keyboard in two so my hands can hold the tablet and type fast at the same time. I will note there are times such as work where I prop it under my desktop monitor and don't want to have to keep grabbing for it, so I use a bluetooth keyboard I got from Microcenter for $24. Most of the time though it is in my hand. If you don't mind some money, I'd look into some of those foldable bluetooth keyboards. Folded about the size of a cell phone but unfolded a good keyboard for even someone with big hands. Didn't go that route and it bites me in the butt sometimes.
On the case issue...
Getting a case isn't just about the nice feel of leather but what you are going to use the device for and how the case will function and hold up to the use you are going to put it through. I'd suggest in your case getting a neoprene sleeve with some padding to it. While I was waiting for my first case to come I had my Nexus 7 in my 10inch neoprene and made homemade padding into the sleeve since there was an extra few inches. Not functional for most people but since you're taking this biking more protection the better and you won't be pulling it out every few minutes like me where I'm walking and carry it in a pocket take it out, then put it back and so forth a lot. The case I'd suggest as long as WHILE you are riding, the choices are endless as of late. If you'll be using it for watching videos, just make sure you have a sturdy stand. I got one of those soft covers with hard back cases and it was a pain after a while because the soft cover doesn't roll up so well.
Bought cases for other tablets that were exactly like this, my mom love this compared to the one above that was suggested, it gives it a bit of give and when closed protects it as it fell from the fireplace to the floor a few times.
PU Leather 360degree Rotary Case Adjustable Angle Stand Cover for Google Nexus 7 | eBay
Facebook
Twitter
Instagram