Oh, you've got it good if your commute involves an off-road trail AND showers. Next thing is to figure out your rain gear. At least, pack an emergency cheapo plastic rain poncho.
Kudos for thinking outside of the box! Your health, wallet and the environment will only benefit.
And that's a decent bike. With that crate on the back, and a knapsack/backpack, you are all set to start doing groceries with your bike!