The thing about walking, is its not something you "come up with". It's a style of playing, that is completely improvisational. You know the changes, and you start playing. You use passing tones, either diatonic or chromatic and you walk the bass to the next chord.
The goal in most instances is too extend the lines in a single direction for as long as you can, and then bring it back. The most interesting lines rarely hit the root on '1', but builds tension throughout the changes with note and rhythm choices, releasing it when you resolve to the root. You aren't avoiding the root, but even if you hit it on '2', the release is palpable and entertaining.