Joe waved to his mom and headed toward the school bus.
Or: Joe waved to his mom and headed towards the school bus.
The difference is one of several between American English (AmE) and British English (BrE). No need to get into a spat over it. Just know your audience and write and spell appropriately, recognizing that there are differences in usage and spelling when you cross the pond (and the Canadian border).
According to both CMOS and Garner’s A Dictionary of Modern American Usage, the preferred American form is without the s; with it in British English. Toward is one of several directional words: upward, downward, forward, backward, and afterward. Garner notes that AmE makes an exception to the sans s with afterwards and backwards. In the case of these two adverbs, adding the s is perfectly acceptable.
What’s not acceptable is using to in place of toward. Toward indicates movement. Someone or something is moving in a certain direction. Use to when the meaning is against. For example:
The senator spoke in opposition to the bill.
While it would be redundant to say, “the senator spoke in opposition against the bill,” you could say “the senator spoke against the bill.” It means the same thing.
But if you decide to get away from it all, head toward, not towards the hills.