The main idea stems from the fact that a lot of people like to walk, run, or ride their bikes to work. However, their work may not provide a place to shower. Or perhaps you just want a better shower and bathing experience that isn't provided elsewhere.
It’s an interesting concept and the next step is to qualify it further with some market research.
Where will you find your potential customers for services? My initial assumption would be in a relatively dense urban setting where people want to commute to work or school by biking, or otherwise on their feet, and they need access to a shower and a place to change clothes. I recommend surveying the nearest metro area (New York, San Francisco, et cetera) which is close to you and look for a traffic pattern that would support providing the services. Maybe there is a neighborhood of office buildings or a university where there are inadequate showering options for commuters. I think you could do a site survey for a few places, to see what you learn. You might also consider spending some time at the bike racks and talking with bicyclists to see how they are dealing with the issue today. Is there a need for what you would like to provide? How much would they be willing to pay?
You can also scout out the real estate to determine the costs of creating a facility with the tenant improvements necessary to serve your customers. Conversely, maybe the business is brokering existing shower or bathroom facilities at businesses or at residences with your customers in a manner similar to Airbnb. Maybe the business is providing portable showering facilities by converting RVs so they 2-3 sets of showers, then you can serve weekday commuters but also provide services at local festivals where there are no services.
It’s hard to say what the results will be but I believe doing some market research will give you a better sense of the viability of the concept. You may well uncover other unmet needs that you could serve better than your original concept. If you can identify a basic value proposition to get started, then you can iterate from there.