Gamma Rays don't allow Hulk to grow a mustache. He would need a huge saw to shave his mustache, same goes for his hair. 

Rulk doesn't like mustaches, so he puts makeup over it like Cesar Romero.

The gamma radiation could be the culprit, unless the Hulk's facial hair recedes into his face upon transformation.  This could also contribute to him being more angry I would think.

The fact that Rulk doesn't have a mustache has always bugged me.
I understand that Rulk having a mustache would have been a dead giveaway (pre issue #23), but some attention to detail would have been nice. Thunderbolt Ross should be clean shaven.

" The fact that Rulk doesn't have a mustache has always bugged me.I understand that Rulk having a mustache would have been a dead giveaway (pre issue #23), but some attention to detail would have been nice. Thunderbolt Ross should be clean shaven. "

Marvel has had a long tradition of pseudoscience by which they drop a term like "gamma radiation" or "cosmic rays" and then give it inconsistent magical properties.

The radiation stunted the hair growth in the chin...?

...... and I've never seen Hulk go to the bathroom..

John Byrne addressed this sort of tangentially when talking about his termination from She-Hulk [edited to be more on point...]
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QUESTION:

I recently picked up Sensational She-Hulk #7, and I got to thinking.... Is this the basis of the disagreement with Bobbi Chase over the scene of Jen shaving her legs and breaking blades? (For the uninitiated, the story resolution in #7 has Shulkie undergoing an electrolysis treatment, which is specifically referred to as permanent, therefore there would be no leg hair to shave in the first place, let alone break razor blades against.)

ANSWER:
. . .
On top of this was the scene with She-Hulk shaving her legs. Now, let me state up front that I have an instant prejudice against this sort of scene. I just don't like 'em. Not sure why, just don't feel they are necessary to the development of the characters. However, in the context of this particular scene, the "development" was to show that Jen was an idiot. Sitting in the tub, shaving her leg, she immediately breaks the blade. So she grabs another razor, and breaks that on the first stroke. So she grabs another, and breaks that. And another. And another. The "punchline" is to see a huge pile of broken razors by the tub. My objection, of course, was that Jen would not do this (even if she needed to shave her legs, which arguably she did not). The first time she tried, the first time the razor broke, she'd get on the phone to her pal Reed Richards and say "Here's my problem..." Reed would have an Atomic Leg Shaving Apparatus (which, knowing Reed, would be big as a Volkswagen) delivered to her apartment within the hour! Problem solved.
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Source
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The meta answer is "depends on the writer" (and the influence tradition may have on him or her). 
 
In-story, you have to address two questions: 1. How does Hulk default to a particular appearance?; 2. How does Hulk change that default appearance? 
 
With respect to the default, I tend to like the "RSI" (The Matrix) type logic, that psychic element that has accounted for the variable size, strength, savagery, smarts, & shade of the Hulk over the years.  You can argue that being clean shaven but with a mop of hair above is just what comes to Banner's subconscious mind and that Ross either thinks the same or- in years of hunting Hulk- has come to have the same image buried in his subconscious.  We know that whether Banner shaves his head, puts a bullet in himself, or Ross wears a mustache... when they transform they will revert to the default (I've not read enough Hulk to know, but has anyone ever lost a limb before transforming?).  So whatever hairstyle preference of Banner or Ross is just as irrelevant as any injury they might sustain. 
 
But to change that we're in more murky territory.  Our only data-points are the Maestro, Hulk off-spring in OMW, and She-Hulk shaving and infuriating Byrne.  RSI could account for all three- Maestro either thinks himself evil or aged, the spawn of Hulk having their own RSI, and Jenn's RSI matches her perception of what womanhood ought to entail?  But there are also other common factors.  In all three cases, the hulk-type has been in their form for an extended period of time.  Maestro doesn't revert back to Banner AFAIK, the spawn stays hulked up to survive the post-apocalyptic landscape, and Jenn was stuck as She-Hulk... so then the argument would be if you remain Hulk long enough, you can just grow hair and trim it.  A final common factor is the external variance on their mutation.  Maestro was dosed with radiation, the spawn was produced through reproduction, and Jenn through blood transfusion... these differences may account for their ability to grow hair.  Additionally, it could be a combination of all three. 
 
Honestly, though, I don't think the writers thought about it too much! ;-) 
 
Edit: Seeing Versa's post below gives us a fourth data-point and removes the third possibility if normal Hulk grows a bears without any extra effects acting on him... and I would tend to think he would not be able to adjust his RSI that much on a whim... so the most likely answer- if trying to stay more consistent than the writers- is time spent staying as Hulk with off-panel shaving.

your thinking of growing a mustache aren't you G-Man :) 
 
I'm kind of surprised that in the marvel universe there wasn't more staches. Given it's a trademark of Stan Lee, you'd think they'd have used it more.

I remember plenty o' times seeing Hulk, in the 90s/early2000s' run having some not-full grown beard, scruffy, some facial hair... And like the others said, in Old Man Logan, in the End, in many other stories we've already seen Hulk with some facial hair.
 
Hulk can.
 
Now, Rhulk, that's a whole other question, I call it "plothole" on Jeph Loeb's part, or why you shouldn't improvise the answer to a mystery like Red's real identity/Ross.
(come on! It was so improvised! There were clues to him being Ross, yeah, but also to him being any of the other characters from Samson to Shield agents to Rick who turned out to be the A-bomb.. I'm sure he left the field open enough to improvise who should have been Rhulk in the end...and used "fake" Ross-androids in his plot to ease that solution)

Because he looks like a giant doosh with one! Just look at 'im!

I've said it before and I'll say it again, Red Hulk should have a moustache.  It really makes no sense that he doesn't.  If the person that turns into the Hulk has a moustache, then the Hulk should in turn have a moustache; it's not as if the Hulk is bald, he has hair prior to and after transforming. 
Maybe it was because slapping a moustache on Red Hulk would have given a giant clue as to who Red Hulk was, but now that the secret's out, they should give him one.

...I gotta say, Hulk looks pretty good with a stache. 

The transformation resets their puberty, which would also explain the urge to smash things.........

" The fact that Rulk doesn't have a mustache has always bugged me.I understand that Rulk having a mustache would have been a dead giveaway (pre issue #23), but some attention to detail would have been nice. Thunderbolt Ross should be clean shaven. "

" it's not as if the Hulk is bald, he has hair prior to and after transforming."

"
The real reason?   
 
It is due to the fact these guys have the market on mustaches sealed tight:   
 
 

"

Ok here is my solution to that problem...... Hulk and Banner can both grow beards.....
 
But they both have a seperate skin profile...witch must have time to grow hair....
 
In case of when Banner would be human for long....and he didnt shave...he got a beard....
 
But , when Banner changed into Hulk that skin needs the same time to grow hair as his human form... And since he doesnt stay "Mindless Hulk" for long...the "Hulk-skin"  never had time to grow facial hair. When he was "Smart Hulk" ... (Like in Planet Hulk) he was Hulk all the time, but was smart enough to shave..  So both Banner in his Human and Hulk persona can get facial hair..
 
So, do I get a No-Prize now or ......:P

" The fact that Rulk doesn't have a mustache has always bugged me.I understand that Rulk having a mustache would have been a dead giveaway (pre issue #23), but some attention to detail would have been nice. Thunderbolt Ross should be clean shaven. "

Its really as simple as this: they didn't want to give away who rulk was so they had to lose the mustach. Now since everone is aware of who he is, i say thunderbolt should rock the stach in hulk form for sure.

" @DMC said:

" The fact that Rulk doesn't have a mustache has always bugged me.I understand that Rulk having a mustache would have been a dead giveaway (pre issue #23), but some attention to detail would have been nice. Thunderbolt Ross should be clean shaven. "

Although i don't really know that much about the Hulk and the Marvel Universe, even i could have guessed that it's General Ross if Red Hulk had a mustache. But if if thunderbolt all of a sudden wouldn't have a moustache anymore, it also could have been a clue too much to who he really is.  "