When you think of Romans taking a bath, of course the first thought is of the large public bath houses. But honestly, would that really be for everyone? Aristocrats, delicate ladies...they might not be on board with soaking alongside the hoi polloi. Private bath facilities clearly existed alongside the public ones. Perhaps in the comfort of one's villa? Or in upscale executive suites at the public baths? And for those purposes smaller scale bath tubs would be needed. In fact given the same dimensions of the human body then and now, you would expect them to look a lot like today's fixtures.
The problems associated with a study of Roman bath tubs are several. There were probably not all that many of them. They were often re-purposed as baptismal fonts, or as watering troughs for livestock and so forth. It can be hard to tell the simpler ones from your basic sacrophagi or from vats used for industrial purposes.
Context helps. Here for instance is a "private" bath tub from Pompeii.
And to get back on topic, here are several on display at the Baths of Diocletian. I am assuming that they are from the site.
The last one of course is not a proper bath tub. More of a hand washing station but I liked it enough to include it.
Now, if you want to see some impressive Roman bath tubs you need to go across town. Check this beauty out:
Welcome to the Piazza Farnese. This is the open space in front of the former Palazzo Farnese, a High Renaissance palace built by the Farnese family to show their considerable affluence and prestige. (It is now the French Embassy).
Out front some swell decor was needed so a pair of over sized bath tubs were acquired. The best evidence suggests they came from the Baths of Caracalla, and were made of Egyptian granite. You could clearly fit a number of bathers into one of these, sort of the Roman Imperial version of a hot tub party.
All of these examples are fine of course, but seem to lack a certain...Patrician fashion sense. Contrast them with this nice example in Egyptian red porphyry that serves as a baptismal font in the Milan cathedral!