In the very first episode, Rick escapes from hospital, finds a bike, cycles to his home - and throws the bike away.
Apart from that, I think facing a bunch of zombies is safer within a closed car. And if you need both hands free for shooting or handling several weapons, you would also prefer not to sit on a shaky bike. I'd rather stand on my own feet or sit in a car. Or (in a pinch) on a nice, high and fast horse, like Rick in episode one.