I usually see bikes freestanding (with ratchet straps or something similar) in the backs of pickups. I have also seen a simple rack made from 2"x4"s in the bed behind the cab. There's bound to be a simple DIY answer for you somewhere. Try these for inspiration:
I have a truck but it has a topper and bikes don't fit standing up.
Here's an alternative to putting the bike in the bed. Its made from 3" channel and a slide in hitch. Easier to load and unload than getting the bike up/down from the bed. Just a suggestion.
I just stand mine up straight in the center, with bungee straps holding it in place from each side. Then again, I have a bunch of tie down rings added to the back of my truck.