Good morning. I still didn't get the photos, so I'm going to go ahead without them. There are several possibilities when a rabbit loses fur like this.
Shedding in the fall is quite common. Losing large amounts of hair and bald spots appearing are also not unusual. I've found that individual rabbits may have a different shedding pattern from year-to-year. They may shed heavily in the spring one year, but not until October the next. shedding is influenced by day length and by the rabbit's hormone levels.When the skin looks healthy and normal, heavy shedding isn't a problem.Look closely at the bald spots. If you see new tiny downy hairs coming in, you're probably dealing with shedding. If teh skin looks normal, but no new hairs are coming in, you may be dealing with an endocrine disorder. Thyroid disorders, especially, can cause extensive fur loss.
Let's look at other possibilities. The rat may have brought in a parasite or a fungal infection.
If it's very flaky - like a bad case of dandruff - you may be dealing with fur mites. If the skin looks red and sore, that might be an infection. Mange is another possibility. A vet is needed to treat any of these conditions. Rabbits are sensitive to many medications and can even die if some (Like Frontline) are put on them. You can read all about normal and abnormal fur loss at this site:
This site has a directory of rabbit vets, if you end up needing one:
While normal shedding, parasites, and infections are all possibilities, all the bating is probably a factor. Rabbits are not like dogs, and do not need to be bathed. In fact, it is recommended to never bathe them. They keep themselves very clean, and bathing completely strips the skin of its normal oils and dries out the fur. That can lead to fur loss. A bath is stressful to a rabbit and many of them will even get sick after being bathed. Yours is apparently an exception to that, but baths are still not good for him. I have owned hundreds of rabbits, and have never given one a bath. If a rabbit has diarrhea or gets into something messy, we may gently wash off the soiled part of the body, but not bathe the whole rabbit. You can confirm this information on the following sites:
In summary, here's what I recommend. Examine the skin carefully. If it looks normal and new hairs are coming in, there is probably not a disease or parasites. If you see flaking skin, sores, redness, etc., or if no new hairs are coming in, schedule a vet appointment. Stop giving baths. Make sure your rabbit has a clean soft bedding that is paper-based, such as CareFresh. Wood and corn-based litters irritate the skin. If your rabbit lives outdoors, make the bedding extra deep to keep him warm as the weather cools this fall.
If you have more questions about this, let me know in a REPLY. I hope your rabbit will soon have a new full coat.