"Bodily" appears in dictionaries as an adjective. The Collins COBUILD Dictionary of the English Language* lists these word combinations in their examples: bodily needs. bodily functions, bodily harm. The American Heritage Dictionary of the English Language** defines the adjective "bodily" in this way:
"1. Of, relating to, or belonging to the body. 2. Physical as opposed to mental or spiritual: bodily welfare."
("Bodily" is also an adverb – not part of your query -- defined in the Collins COBUILD in this way: "You use bodily to indicate than an action involves the whole of someone's body: I was hurled bodily to the deck.)
"Body" does not appear as an adjective in these dictionaries. It appears only as a noun. However, it is clear that "body" is often used as an adjective in certain collocations.
While not listing "body" as an adjective itself, the Collins COBUILD does have entries for noun + noun combinations using "body" as the modifier: body armor, body blow, body clock, body language, body odor, body search and body stocking. In all of these word combinations, however, the second noun does not belong to the body, but are for or about or from the whole body.
In The American Heritage Dictionary, "body" in a noun + noun construction includes some of the above word combinations and also these: body bag, body cavity, body cell, body fluid, body image, body louse, body mechanics, body shield, body shirt, body shop, body snatcher, and body suit. Of these, only "body cell" and "body fluid" (must be an alternative to "bodily fluid") could be considered "belonging to the body."
"Bodily" appears in the following noun + noun constructions in the Collins COBUILD online concordancer*"
bodily agitations, bodily ailments, bodily changes, bodily coordination, bodily control, bodily death, bodily functions, bodily harm, bodily injury, bodily movement, bodily orifices, bodily parts, bodily processes, bodily sight, bodily strengths, bodily symptoms, and bodily thoughts and passions.
40 random examples are given in the concordancer, so "bodily" readily appears directly followed by the nouns it modifies. However, in the 40 examples of "body," most are of "body" as a noun. The following instances do appear, though, with "body" as an adjective:
body parts, body pressings, body shop, body style, and body weight.
It appears that when the adjective could mean "belonging to the body," it is possible to use "bodily" as well as "body": body/ bodily parts, body/ bodily ailments, body/ bodily fluids. Depending on the context, too, you might use one instead of the other:
My bodily parts are hurting from the four-day car trip. ? (Part of one whole body)
There were body parts near the scene of the accident. ? (Not part of one whole body,)
"Body," but not "bodily," seems to be used to describe something that happens to all or part of the body, or, that treats the whole body: body image, body shop.
There does not appear to be a sure differentiation, but the Grammar Exchange would be pleased to receive contributions on this topic from you readers.
P.S. Marilyn Martin writes that she has done a Google search and found lots more examples for "body fluids " – 316,000 – than for "bodily fluids," which yielded 87,000. She says that she doesn't know what this proves, except that "bodily" isn't is so many people's vocabularies, possibly.
* The Collins COBUILD English Dictionary. Harper Collins. 1995.
** The American Heritage Dictionary of the English Language. Houghton Mifflin Company. 1996