Just a few stray particles of pet food are enough to lead a parade of ants through your house. Before resorting to chemicals to get rid of them though, try using a pan of water as a moat to keep them away from the bowl.
Ants aren't particularly good swimmers, so a shallow tray of water will dissuade them from marching an entire colony through your house to get a few crumbs of kibble. If you feed your pets outside, this tip is even more important to keep them from getting bitten. Depending on how excited your pet gets about food, you may also want to set a towel underneath the tray to soak up any splashes.
Ants or not, the tray can also double as an extra large water bowl, saving you a few trips to the faucet. For some more clever pet tips, check out The Family Handyman's list through the source link.
Hints and Tips for Pet Care and Pet Safety [The Family Handyman]