Is there any rules that govern when to use 不 and 非 and 無 and 未 in regards to the meaning of "not" or "un-"
for instance 非表示, 不満
It's not so much that there are rules, it's that the different kanji have different meanings which might help determine which one is the right choice. Note, however, that the reality can be flexible, so be aware that there can be exceptions and conventions that differ.
These kanji have the following meanings in prefix form which can help shape the meaning of the terms they are modifying:
*Note that the kanji
Hope that helps.
My answer is almost the same as Dave's in principle. I hope it brings something new to the table by introducing the notion of "transcribing" Kanji words into Japanese:
When I studied 漢文【かんぶん】 in my high school days, I learned that transcribing kanji words into full Japanese phrases can help understand them better. Kanbun is "a Japanese method of reading annotated Classical Chinese in translation" (Wikipedia).
If we combine 表示 with each of the four characters 不・非・無・未, and skip the details, they get transcribed as:
不表示 → 表示せ不 (ず)
非表示 → 表示に非ず (あらず)
無表示 → 表示無し (なし)
未表示 → 未だ (いまだ) 表示せず
In theory, if you reverse this process - by finding the right phrase using either of the four Kanjis that matches your intention - you should be able to get the correct Kanji compound word.
Note 2: In case of 表示, "不表示" and "非表示" don't have much difference in meaning, although 非表示 is the prevalent one. My guess is that 非表示 is more neutral, and therefore more versatile and widely used.
Despite the question seems to have reached its own solution, I'd like to make a new answer, for I find the existing explanations would not lead to a correct understanding on this topic.
Each of these words has their own meaning, which usually cannot be directly translated to English affixes like "non-", "in-", "un-", or "-less", so I'm going to explain these terms descriptively.
What they have in common is negative meaning and ability to attach to 漢語 (Sino-Japanese) words.
However, existing words with these prefixes often betray your expectation on how it works, mainly because:
Samuel Martin's A Reference Grammar of Japanese has a good summary and discussion on those prefixes, but note that he has erroneous analysis on some words regarding the said matters.
Acknowledgement: Thanks to @snailboat for references and advice.
I have a partial answer for 不 and 無.
For a na-adjective, 不～ can be interpreted as ～ではない
For a suru-verb, 不～ is ～しない
For either a noun or a suru-verb, 無～ can be interpreted as ～がない
(Source: Bojinsha's Intermediate Kanji Book, Vol 1, chapter 2)