Probably more inertia than magnetism. The water isn't stuck to the bowl as a solid mass. Rotating with the bowl requires the water to drag on itself to move with the bowl. That takes time for enough force to transfer to really get the water rotating at any significant speed, so it merely looks like it's acting like a compass. If you keep rotating, the water will eventually catch up to the bowl's speed.
Mind, anything floating on the water could also actually act like a compass needle if it has a strong enough charge differential across it. That's not uncommon at all, it'd just be weird for spit or a collection of bubbles to have enough charge since they're bad at holding charge.
The test would be to spin around once or twice with the bowl and set it down. If it is not magnetic, the water should stay rotating very slowly and the slobber/etc will just continue to rotate a little and eventually stop and sit at a new orientation. If it IS acting like a compass, the floaters will slow down and then rotate back the few degrees the other way to stay oriented.