I guess the answer may be different for rich people who had their own baths and others who visited the public baths.
Your guess is correct.
Bathing in Rome was one of the common daily activities. While nowadays bathing is seen as strictly private activity, bathing in Rome was a public activity. Rich Romans could afford themselves bathing facilities in their villas, while other classes bathed in thermae, public facilities for bathing, similar to nowadays spas. They were owned by the state, and they sometimes covered few city blocks. Largest known thermae were Baths of Diocletian. Each emperor tried to out-do his predecessor, making his bath more spacious, more splendid, more popular. In thermae people could socialize, and normal daily activities were done there.
Baths were very important to Romans (in catalogue of buildings in Rome from 354 AD there were documented 952 baths in the city)! There were an average of five bath houses for block and one balneum for every 35 apartment buildings.
Balneum, small bathhouses, could be privatly owned and people could take a bath there with reimbursement and they were designed primarly for neighborhood. Popularity of balneums prompted Agrippa to build a massive, centrally located bath house.
As Thermae were place where people could talk, socialize and make business an average Roman would go there once a day. After Forum Romanum, thermae were the largest hangout in the city. Rich Romans normally bathed once a day, but their goal was to keep themselves clean, rather than socializing and listening city gossips.
From "Role of Social Bathing in Classic Rome" by P.D. and S.N.:
In early Roman history, bathing was done every nine days and was not seen as a priority. During the 2nd century BCE, however, the Greek custom of regular bathing reached Rome (Mertz 357). It gradually became a daily practice for Roman citizens, regardless of their financial standing, to frequent public baths.
But, that evidence doesn't prove us that Romans were clean people. We should keep in mind that Romans had no chemicals to keep water clean and we have no idea how often the water in thermae was changed, although there were some public baths which were constantly supplied by clean water. Also there were a lot of other problems, like simultaneous bathing of sick and healthy people, bad smells of furnaces and smoke and dirty water. Marcus Aurelius in his Meditations said:
What is bathing when you think about it - oil, sweat, filth, greasy water, everything loathsome.
The regularity of bathing in Ancient Rome really depended on your gender or social status to a certain degree. This was due to the costs and times allocated to men and women and perhaps even depending on your social status. This may have varied as individual bathing houses may have had different rules.
The wealthier classes were able to afford to build the facilities in their own homes, as well as the water required to fill them and so could bathe more regularly, especially as they may have also had more leisure time available to them.
The middle or lower classes on the census on the other hand would have had to rely on the balneae or thermae, this would have meant taking time out of a potentially busy work schedule to visit and pay for a bathing session which may not have always been practical.
So it's hard to generalise when talking of the Romans as it would have depended on certain factors, some of which I have mentioned above. Yet it seems that given the opportunity they enjoyed visiting these complexes where various leisurely activities could be undertaken.
For some more information on the Romans' bathing habits have a look here.
I have not made a study of this so can only add a couple of snippets to what others have said.
Raoul McLaughlin 'The Roman Empire and the Indian Ocean' commenting on how epidemics could spread more easily among the crowded Roman population than in the more thinly populated barbarian areas beyond the frontier, mentions the Roman habit of communal bathing as one of the reasons.
Also, I once attended a talk by an archaeologist who mentioned the irony of excavating the remains of luxurious Roman baths in what is now a remote part of Turkey, when all the archaeologists excavating it 2000 years later had for washing was a primitive improvised shower (basically, tip a bottle of water through a sieve). In some respects, civilization seemed to have gone backwards in the intervening millennia, not forwards!