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:
非 【ひ】 Means opposite* (as in: reverses the meaning of the word).
無 【む】 Means absence (as in: it was never there).
未 【み】 Means incomplete in the sense of not having achieved (as in: we have not yet reached it).
不 【ふ】 Means incomplete in the sense of not yet having reached capacity (as in: the glass is half empty).
*Note that the kanji 非 actually originally means "error", but that has negative connotations that don't necessarily apply when it's used as a prefix. "Opposite" is a better guide.
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.
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)