It was funny the first time.
Unfortunately its gone past overdone and is sadly now well into the land of creepy, where it has multiplied. Typical scenario goes thusly:
A) Lady posts attractive pic of herself.
B) Casual male acquaintance responds by leaving an open comment with the above quotation. Possibly with a winking emoji if they’re feeling particularly clever.
C) Nobody bothers pointing out that it’s not fun when a casual acquaintance announces they’re about to vigorously masturbate to the lady’s image without further ado.
And the conversation usually comes to a screeching halt there. Even if there are those willing to point out, “He’s Adam Baldwin playing a character. You, nerdboy, have proven you can’t so much as spell ‘respect,’ despite the fact that Aretha was kind enough to put it to music before you were a gleam in your daddy’s nutsack,” there ain’t much in the way of offenders willing to listen.
This is usually where I get trapped in a cyclical argument with our examplatory fuckin' nerdboy, trying to convince him that I haven't been hoarding the panty-dropping cheat codes. However, since this is a case of emulating a pop culture figure, we have an example we can study and analyze. More fortunately, thanks to the sadly limited nature of the media, it's easy enough to rewatch both Firefly and Serenity (Twist my arm, really), to get at what the character's up to.
So how does the hero of Canton express his lechery?
The pilot episode has him making a crass comment about Kaylee at the dinner table. While Mal pointing this out has Jayne doubling down, he shuts up and obeys when his refusal to back off gets him banished from the table. While more graphic than most examples throughout the series, it does set the pattern for how he acts around the rest of the crew. Reactions consist of either friendly banter or an indication that he needs to back off and shut up. Lo and behold, HE BACKS OFF AND SHUTS UP!
WASH: Captain, can I have money for a slinky dress?"
JAYNE: "I'd chip in."
ZOE: "I can hurt you."
JAYNE: SHUTS UP
JAYNE: "What we need is a diversion... I say Zoe gets nekkid."
JAYNE: "I could get nekkid."
JAYNE: SHUTS UP
ZOE: "Is that Jayne? Wash, pinch me!"
JAYNE: "I'll pinch you."
ZOE: *waves him off*
JAYNE: SHUTS UP
in "Trash," ...
JAYNE: "Well, as a rule, I say, girlfolk ain't to be trusted."
RIVER: "'Jayne' is a girl's name."
JAYNE: "Well, Jayne ain't a girl! She starts in on that girl's-name thing, [reaches into his pants] I'll show her good 'n' all, I got man parts!"
SIMON: "I'm... trying to think of a way for you to be cruder. I just... it's not coming."
JAYNE: SHUTS UP
Not once does he bitch about his right to continue acting this way. In fact, Jayne rarely displays any sort of outward interest towards the women of Serenity, and definitely doesn't pursue any of them. When he does show interest, it's almost always initiated by someone else, such as the idea of Zoe in a slinky dress above, or "I could stand to hear more" about Kaylee "not having anything twixt my nethers weren't run on batteries."
In fact, much of his interactions run more to the practical. In the above example from "Shindig," Jayne behaved with much more interest to distracting Badger's men than out of prurient interest in seeing Zoe naked. We see more of that in "Our Mrs Reynolds," when his immediate reaction to Saffron is more of seizing an opportunity than anything else.
MAL: "I don't know this girl!"
JAYNE: "Can I know her?"
... Followed by yet another example of him shutting up when shut down. Later in the episode, he offers to barter Vera. Played for laughs, obviously, but think about it for a second: Jayne NEVER could have afforded a weapon like Vera on his own. He had to kill SIX men who were coming for him in order to acquire Vera as a trophy. In his eyes, he's offering more than he can ever earn at once.
His practicality reasserts itself in "Heart of gold," when he makes sure to train his chosen playmate into duty as his A gunner before jumping into bed (or not bothering and staying in the chair, as it were).
Which leads us full circle into the phrase that got us into this in the first place: "I'll be in my bunk."
Jayne says this exactly twice: once when the counselor arrives as he's looking from the galley hatch on the far side of the cargo bay, once as the counselor leaves while Jayne is spotting Book on the weight bench near that same hatch. While not exactly sotto voce, he's not saying it with the counselor in earshot, either. The only ones close enough to hear him are Book and Kaylee, neither of which comment.
The online equivalent to Jayne's use of the term, "I'll be in my bunk," would be a PM to a mutual friend.
Examplary nerdboy's typical use of the term, however, is the equivalent of saying it over the shipwide PA system and broadcasting over the cortex simultaneously.
The long and the short of it is, there is a time and place for everything, including appreciation of eroticism. I’ve got my preferred terms and delivery methods, which I’m not pointing out here.
After all, an ethical scoundrel needs a few secrets of his own.