Water in the ears will not cause an ear infection unless your pet has an underlying condition in their ear. The most common condition is an allergy. Allergies often cause the ears to produce too much wax and induce inflammation as noted by redness. This mildly inflamed ear, if exposed to water will usually become more inflamed and infected. So, if ear infections have been recurrent for your pet or they develop after bathing, please schedule an appointment with your veterinarian.
I bathe my dogs and cats by wetting their body and legs and then lathering. I avoid wetting their head until the end of the bath. A wet head results in shaking of the head and then the body follows. Everybody gets wet. When its time to wash the head, a towel on the trunk will limit the shaking and keep you dry. You may also place large cotton balls in the ears to absorb any misplaced water. Be sure not to push the cotton deep into the ears. Some of my pets don’t mind the cotton balls; others want to shake them out. If you do get water into the ears, several good headshakes will disperse the water and the rest will be quickly absorbed into the skin of the ear canals. The skin of the ears is just like the skin on the body with additional oil glands.