that just sounds the nuts. lol
why not have bikes that you can ride on/pick up along the way, and ride around attacking zombies, I also like the idea of a squad or team base game, so you could have a team fighting on foot wile you go ahead and clear the path of though the zombies, if I remember a baseball bat and chains were the weapon of choice in road rash, so you could elaborate on that.
maybe the goal of the game is to clear the path just so the team can get though, you could have air strikes like in streets of rage, which your team could bring to the fight, plus you could upgrade your weapons and bike, as well as the player, but don't get knocked off your bike or the zombies start hordes at your position, and you could get off the bike when ever you want, fight face to face, and call for back up from your team.
turn base may be tricky for a game with a bike in, so ever go with a bike in your game or drop the idea of bikes or turn based game.
I hope this helped
Soul sucking devils, twisting the body's of the damned, slivering slim drips from every poor, sin licking at ears, and a smell so bad it stings the eyes, welcome to the darkness.