Well, this is an...interesting question. But I'll do my best to answer with a ssingle pun.

Our knowledge of ancient ideals of beauty comes largely from visual sources. So if we are to gauge just how much derriere was deemed desirable, we have to rely on sculptures, mosaics, and (where they survive) paintings. Artistic convention, as we'll see, was at least as important as representing reality; but such representations do at least suggest how the Romans liked to fantasize about themselves.

I would guess that you're asking about women. But let's start with men (as the Romans surely would have), since this will allow us to comment a bit on method. As you mention in your question, statues of Greek men in the Classical period tend to be show every subject as a lithe, toned, and youthful athlete. The bodies of these sculptures may have genuinely corresponded to the gym-sculpted flesh of some Olympic champions. In most cases, however, we should see their nudity as a sort of costume, a way of communicating something about the man. The invariably undersized genitals proclaim the subject self-mastery. The smooth muscles of the upper body suggest dedication to a training regimen (and, more generally, to the citizen ideals of the gymnasium). And the bulging buttocks (visible in, for example, the famous Riace Bronzes) bespeak the surging strength of a sprinter and warrior. (Such buttocks were also deemed desirable in boys, as Mr. Good Argument in Aristophanes' Clouds uncomfortably reminds us).

When Roman men began to commission nude statues of themselves, they inherited and imitated the Greek conventions for musculature, bulging rump and all. Most nude statues of Roman men belong to the emperors (nudity was a mark of divinity, among other things); and to judge from that admittedly limited data set, we might infer that Roman men wanted to be seen as perfectly-muscled demigods. This, however, would be misleading. Most Roman men probably wouldn't have objected to being perfectly-muscled demigods. In reality, however, few were so committed to the gymnasium. Bulging muscles were for gladiators and laborers; the gentleman should be fit, not jacked to the gills. Artistic conventions, in short, were not necessarily standards of beauty.

We need to keep this caveat in mind while assessing, at last, how Romans idealized the female body. To judge from artistic representations, the answer is straightforward: the Romans preferred broad hips and small, firm breasts. The Roman interest in peachy bottoms is on abundant display in the famous mosaic of Cupid and Psyche from Piazza Armerina, or in the even more famous Venus Callipyge ("fair-bottomed Venus") in the Naples Archaeological Museum. So should we assume that these represent the Roman ideal of beauty? Only with caution. Like their male counterparts, female nudes in classical art are both stereotyped and freighted with meaning. The famous Aphrodite of Cnidus, the first and most famous female nude in Greek sculpture, played an important role in establishing the body standard of all subsequent female nudes. And just as the male nude was intended to advertise potency, so was the female nude (with its conventionally broad hips) designed to showcase fertility.

We should not be excessively cautious here: the Roman ideal of female beauty probably corresponded fairly closely to artistic representations. To a certain point, of course, such representations actually created that ideal, life imitating art. It also helps that we have various and variously lurid literary descriptions of narrators lusting after broad-hipped women, including a very appreciative description of the Aphrodite of Cnidus.

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Hopefully, this answers your question...if you would like to know more about nudity in ancient art, feel free to check out my video on the topic, filmed partly in the Art Institute of Chicago.

It's difficult to speak broadly about social trends like this because the period in which "Ancient Rome" existed was from approximately 800 BC-500AD. Trends change a lot, but I suspect people have always liked asses.

There is one extant piece of writing from the ancient world which is perfect for this, but it requires some explanation, bear with me. The “Amores” of Pseudo-Lucian is a contest dialogue in which two men, Callicratidas and Charicles, debate whether having sex with women or with boys is better. Important to remember in the story is that both of these men are presented by the author as somewhat strange. Most people in the ancient world would be bisexual by today’s standards, so even a man who exclusively liked women was considered odd. The two men come across a statue of Venus, and Charicles, who likes exclusively women, praises her front. Callicratidas, who likes exclusively boys, praises her rear. P-S writes:

"Heracles!" he exclaimed, "what a well-proportioned back! What generous flanks she has! How satisfying an armful to embrace! How delicately moulded the flesh on the buttocks, neither too thin and close to the bone, nor yet revealing too great an expanse of fat! And as for those precious parts sealed in on either side by the hips, how inexpressibly sweetly they smile! How perfect the proportions of the thighs and the shins as they stretch down in a straight line to the feet! So that's what Ganymede looks like as he pours out the nectar in heaven for Zeus and makes it taste sweeter. For I'd never have taken the cup from Hebe if she served me." While Callicratidas was shouting this under the spell of the goddess, Charicles in the excess of his admiration stood almost petrified, though his emotions showed in the melting tears trickling from his eyes.

So the sexuality of the men and of the culture complicate this. Callicratidas is praising Venus’ rear as if it were that of a boy, even going so far as to compare it to Ganymede (a male mythological figure who was abducted by Zeus for being so beautiful) but it’s still Venus, the very female goddess. Odd. Also important is that Charicles seems to also think her rear is beautiful. So even two men presented at the extremes of Roman sexual preference are very much-gender bending within this work. What can we conclude from this passage about Greco-Roman sexuality, specifically pertaining to asses?

Everybody likes asses. Both the guy who likes women and the guy who likes boys are moved to tears by it. They prefer a very middle-of-the-road ass. Not to skinny, not too fat. They also apparently like the thickness of the thighs and the shins to be the same all the way down. The ass is somehow hermaphroditic. Further driving home this point are the words for anal sex in the ancient world. The verb “Pedicare” is partially derived from the word “παις,” which means “boy.” So the very act of anal sex seems to be related to doing so with boys. When you have anal sex with a boy, it’s just anal sex. When you have anal sex with a woman, are you treating her like you would a boy? Interesting thought.

I and other scholars are convinced that for the most part in the ancient world, sex was more about power than it was about any material factor in the sexual act. In a world without Christian morals, sex could really be all about power instead of shame, but that’s beside the point.

Keep in mind that Pseudo-Lucian’s Amores was written in the fourth century concerning Greco-Roman people, so there are seven other centuries and thousands of different cultures which fall into the category of “ancient rome” for which the answer to this question could be entirely different. If another commenter has an example, I would love to see it.

Sources:

Pseudo-Lucian’s Amores in Greek: https://www.loebclassics.com/view/lucian-affairs_heart_amores/1967/pb_LCL432.151.xml

In English: https://people.well.com/user/aquarius/lucian-amores.htm

The etymology stuff I just know because I have a degree in Latin.