The short answer is no, public nudity from Roman women would not have been common, but also there was a lot of tension regarding what constituted proper behavior. Romans were a notoriously conservative society back in the old days and explicitly drew a distinction between themselves and what they saw as the more decadent practices of Greeks and other “eastern” (from the Roman point of view) cultures. Actually, Romans were constantly arguing about this kind of thing; it was clearly a source of social anxiety. Around the time A few generations before the events in this series would have taken place, the Senate introduced legislation to ban/reform the Bacchanalia, for example, which they perceived as a dangerous foreign rite capable of undermining traditional Roman mores (see Walsh 1996: https://doi.org/10.1093%2Fgr%2F43.2.188). (EDIT: I should have added that the mythical female followers of Bacchus were depicted in a kind of animal skin, often partially nude, and engaged in drunken, erotic revelry). Or you can read the writings of Cato, who expresses similar disdain for what he sees as loose morality around the same time.

Of course, a lot of the moral rhetoric from around this time is tied up in the behavior of women. Ironically, compared to Hellenistic Greek culture, Romans were probably a little more egalitarian in terms of gender. Not to paint things with too fine of a brush, but there were no explicit laws or customs that forbid women from eating with men, going out in public, or owning property, for example. And while we have evidence that Roman men from around this time were (with all kinds of sexist and misogynistic language) concerned about what women were putting on their bodies (eg, expensive clothes and jewelry, seen as out of step with good ol fashioned Romanness), we don’t see any evidence that public nudity was at all common. People certainly would have been complaining about it if so.

Not entirely qualified to comment on this, but it’s also important to know that nudity in the Roman world was associated with heroically nude depictions in art. Romans were more willing to paint/sculpt nude women than the Greeks, but again, there is no evidence Roman women would ever be seen in public like this.

As for the why these kinds of images are common, I would ask, are they really? Most depictions of the past are stuffy and sterile, perhaps precisely because Victorian morality was so scandalized by the erotic imagery that is so common in Roman art. I believe Spartacus is part of a more recent trend which tries to be less conservative about depicting sex in the ancient world in general, which is a good thing. In this case, however, the show was more beholden to modern tastes/what audiences want to see than historical accuracy. EDIT: It's also fair to point out that even if the over-the-top imagery of Spartacus is exceptional, Romans have long had an association with decadence in the general imagination. Much of this goes back to Edward Gibbon's late 18th century thesis on the "fall of Rome" as a result of moral decline. Gibbon himself was highly influenced by the kind of conservative Roman writers mentioned above, from Cato in the Republic to early Christian writers later on, who complained of extravagance and moral corruption. Images gathered from texts like Patronius' Satyricon, which present, in a very tongue-in-cheek manner, mind you, the absurdly extravagant practices of Roman dining and a keen emphasis on sex and the erotic have surely also contributed to this image.

We do have a specific example of how at least one crowd at a gladiatorial show reacted to female nudity. It's the anonymous account of the martyrdom of Perpetua and Felicitas and other Christians at the arena in Carthage from around 202-203 CE. It's an addendum to what may be substantially Perpetua's diary.

As was sometimes the custom, the victims were costumed as mythological figures to add to the entertainment. Meant to be gored to death by a "mad heifer," the young, upper-class woman Perpetua and her slave Felicitas, who had just given birth

were stripped naked, placed in nets and thus brought out into the arena. Even the crowd was horrified when they saw that one was a delicate young girl and the other was a woman fresh from childbirth with the milk still dripping from her breasts. And so they were brought back again and dressed in unbelted tunics.

Social standards may have been more delicate at Carthage and the account of the martyrdom has probably been enhanced for polemical purposes, but at least here female nudity was taking the "fun" too far.

/u/cafffaro's answer has already addressed female nudity and toplessness, and noted how they related to worries in Rome over the erosion of Romanness. This conservatism often found expression via the concept of mos maiorum (literally "way of the elders," i.e., the old customs).

This anxiety also extended to clothing that was merely revealing, such as silks that were so thin as to be translucent. Here's Seneca (the Elder, not his philosopher/dramatist/political advisor son), writing a couple generations after Spartacus:

I can see clothes of silk, if materials that do not hide the body, nor even one's decency, can be called clothes... Wretched flocks of maids labour so that the adulteress may be visible through her thin dress, so that her husband has no more acquaintance than any outsider or foreigner with his wife's body.

And silk's being an import (from China ultimately, but via middlemen) underscores /u/caffaro's point about Roman notions of the decadent East.

Edit: spelling/minor wording