@Rory Alsop is correct.
First, terms need to be defined.
There are basically 4 parts of the ear. The outside of the ear (what you can move around with manipulation) is called the auricle or pinna. Occasionally it can become infected, and this is called malignant otitis externa. It is relatively uncommon.
The ear canal (the acoustic auditory meatus or the acoustic canal) can become infected; this is called otitis externa (also known as "swimmer's ear".) It is relatively common, especially in swimmers, people who wear ear plugs, people who clear ear wax out with bobby pins, etc. etc.
The middle ear is separated from the outer ear by the tympanic membrane (a.k.a. "ear drum".) The ear drum prevents water from entering the middle ear. However, there is an entry into the middle ear (where the bones that transmit vibration from the ear drum to the acoustic nerve are housed) from the outer world, and that's through the Eustachian tube, the other end of which opens into the back of your nose/upper throat. This tube is what allows your ear to pop when the atmospheric pressure changes (like on a plane.) This is the area where most ear infections occur. An infection here is called "an ear infection" by laypeople, and otitis media by health care professionals. This is by far the most common.
Finally, there is the inner ear involved in both balance and hearing. An infection here ("a.k.a. inner ear infection") is relatively uncommon, but more common in the elderly, is usually viral, and causes you to feel very dizzy with movement (vertigo).
It's very unusual for infants or small children to get otitis externa unless they are immunocompromised or someone is digging around in there with a fingernail, a Q-tip, or other, or they have eczema of the ear. They might get it by swimming in a very polluted river (which is an activity infants and small children do not engage in frequently), but they will not likely get it from bath water.
Far more likely from swimming in a polluted water source is a middle ear infection because the polluted water gets in your mouth (and throat), and some is pushed up the Eustachian tube into the middle ear.
Infants and children have more "ear infections" (otitis media) because their Eustachian tubes are shorter and at a lesser angle than in adults.
In fact, the ear canal of an infant is different from an adult's. It's shorter and it's angled differently (this is taken into consideration during the ear exam.)
A normal baby will not get an ear infection by getting bathwater in his or her ears any more than a normal adult will. If they did, ED would be full of such children every day. It's far more likely that a baby will get an ear infection by getting bathwater in their mouths (because of that Eustachian tube) than in their ear, and that doesn't happen often either. Otherwise every time a baby put something nasty in their mouths, they would get ear infections.
Image source AnatomyArea.com.
If you want to decrease ear infections in infants, you might want to get them vaccinated.
HOW TO USE AN OTOSCOPE
Pneumococcal capsular polysaccharides conjugated to protein D for prevention of acute otitis media caused by both Streptococcus pneumoniae and non-typable Haemophilus influenzae: a randomised double-blind efficacy study
Serotype Distribution and Penicillin Resistance of Streptococcus pneumoniae Isolates from Middle Ear Fluids of Pediatric Patients with Acute Otitis Media in Japan
Influenza A Vaccine Decreases the Incidence of Otitis Media in 6- to 30-Month-Old Children in Day Care